Question

Please, I could really use some help with this pre-calc problem. Any help would be appreciated

Picture Attached.

Answer 1

Multiply the top and bottom of each fraction by sqrt(x) * sqrt(3x+4) and simplify.

Answer 2

so I would multiply 1/2 & 3/4 by that ?

Answer 3

You can factor out 1/2

Answer 4

So I would factor out before I multiply by the square roots ?

Answer 5

Ranga's suggestion is a very good one. If you multiply the given expression by \[\sqrt{x}\sqrt{3x+4)},\], and then divide that product by the same thing, you will have eliminated the two nasty negative exponents. Look for the two common factors of the numerator of this fraction, and factor them out. Try the factoring AFTER following Ranga's suggestion, not before.

Answer 6

But where did the square root come from ?

Answer 7

is it because of the 1/2 exponent on the expression in the parenthesis?

Answer 8

correct. raising to half is same as taking square root.

Answer 9

Without the equation editor working I am having a hard time typing math expressions.

But to start from the beginning, let a = 3x + 4
We have 1/2 { sqrt(a) / sqrt(x) - 3sqrt(x) / sqrt(a) } =
1/2 * sqrt(ax) / (ax) * {a - 3x } =
1/2 * sqrt((3x+4)x) / ((3x+4)x) * 4 =
2 * sqrt((3x+4)x) / ((3x+4)x)

Answer 10

Okay, wait , I should multiply the numerator by square root of x and square root of 3x+4 first then after multiply the denominator ?

Answer 11

See my last comment.

Answer 12

Becki: By multiplying the given expression by Sqrt(x)Sqrt(3x+4), he is eliminating the negative exponents in that expression. He multiplies the denominator (1) by the same quantity so as not to change the value of the expression.

Suggest you try this on paper.

Answer 13

Becki: in answer to your most recent question: YES.

Answer 14

Is this what you mean ?

Answer 15

I think I am getting a different answer. Let me go step-by-step with my previous answer.

Answer 16

Let a = 3x + 4. We have:
1/2 * { sqrt(a) / sqrt(x) - 3sqrt(x) / sqrt(a) } =
1/2 * { sqrt(a) * sqrt(a) - 3 * sqrt(x) * sqrt(x) } / { sqrt(x) * sqrt(a) } =
1/2 * { a - 3x } / sqrt(ax) (multiply top and bottom by sqrt(ax) so as not to have radicals in the denominator)
1/2 * (a - 3x) * sqrt(ax) / (ax)
Put back a = 3x + 4
1/2 * (3x + 4 - 3x) * sqrt(x * (3x + 4)) / (x * (3x + 4)) =
2 * sqrt(x * (3x + 4)) / (x * (3x + 4)) (i)
2 * sqrt(3x^2 + 4x) / (3x^2 + 4x) (ii)

Many teachers and textbooks object to having radical expressions in the denominator and so I can leave it as either (i) or (ii) above.

If radical is okay in the denominator, then:
2 / sqrt(x(3x+4)) or 2 / sqrt(3x^2 + 4x)

Answer 17

Okay so on line 3 where it is 1/2 * {sqrt(a) * sqrt(a) - 3 * sqrt(x) * sqrt(x)}, where did the second sqrts come from ? like the sqrt(a) & sqrt(x)

Answer 18

L / M - P / Q = (LQ - MP) / MQ

Answer 19

Becki:
Ranga wanted to get rid of that x^(-1/2) in the given expression, so he decided to multiply that by Sqrt(x). Result? 1.
Ranga also wanted to get rid of that (3x+4)^(-1/2), so he decided to multiply that by Sqrt(3x+4). Result? 1.

Answer 20

where is highlighted is where I'm lost

Answer 21

Okay I looked over it once more & what was throwing me off was the 3 still apart of the sqrt(x) * sqrt(x). But I realize now that the 3 is from the 3/2. right ? thats why the 3 is still in the numerator ?

Answer 22

yeah.

Answer 23

It is like subtracting fractions:
3/4 - 2/3 = (3*3 - 4*2) / (4*3)
cross multiplying and combining the numerator and multiplying the denominators.

Answer 24

\[\frac{ \sqrt{x}\sqrt{3x+4} }{ \sqrt{x}\sqrt{3x+4)} }*(\frac{ \sqrt{3x+4} }{ 2\sqrt{x} }+\frac{ 3\sqrt{x} }{ \sqrt{3x+4} })\]

Answer 25

Becki: I'd suggest you copy this expression down and do the indicated multiplication. Then simplify by factoring.

Answer 26

The second fraction within parentheses, like the first, should have a "2" in the denominator. My oversight.

Answer 27

Okay so after redoing the problem & getting Ranga's answer, it was marked wrong?

Answer 28

Well, it depends on what form they are expecting the answer to be. Textbooks and teachers differ from what is an acceptable form. That is why I gave four forms. Two without any radicals in the denominator and two with radicals. Each pair has one with factors and another with factors multiplied out.

Answer 29

All four are the same answers but just in different forms.

Answer 30

The original instructions: "Factor completely." I would add to that: "Eliminate negative exponents."

Answer 31

I tried all 4 actually, I have 5 chances, and each time was marked wrong

Answer 32

I hope you did not use the * as I did here for illustration purposes.

The answers I would try are: 2sqrt(x(3x+4)) / (x(3x+4))
or
2 / sqrt(x(3x+4))

Answer 33

No I did not use the *

Answer 34

I will go over the numbers again. In the meantime, can you find out from your notes or textbook what form they want the answer in for similar problems so you can make the last attempt successful?

Answer 35

In the back of my book for a similar problem the answer was 4x^1/2(9x+8)^1/2

Answer 36

it was the same problem just the numbers in the parenthesis are changed

Answer 37

Can't be the same problem with just the parenthesis number changed. here they are getting all radicals in the numerator but we are getting either a radical in the denominator or a radical in the numerator with an expression in the denominator. Can you post the other problem as a link here?

Answer 38

I just substituted a number x = 4 in the problem and x = 4 in my answers and I am getting the same result. Both reducing to 1/4.

Answer 39

Oh, in your answer to the second problem, did you omit a division symbol after 4?
Is it supposed to be: 4 / x^1/2(9x+8)^1/2 ?
That is, 4 in the numerator and sqrt(x)sqrt(9x+8) in the denominator?

Answer 40

OMG, they are using negative radicals!

Answer 41

And that answer was accepted as correct?

Answer 42

Yes sir

Answer 43

Then, try this answer:

2(x)^(-1/2)(3x+4)^(-1/2)

That is,
2 "x raised to minus half" "(3x+4) raised to minus 1/2"

Answer 44

Be careful since this is the last attempt. If you want you can show me a screen shot before submitting.

Answer 45

Go ahead and submit it and let use see what it says.

Answer 46

It was right!!! thank you so much.

Answer 47

can you please explain how you did it with negative radicals ?

Answer 48

You are welcome. We got this answer a long time ago just a different form.
Sure I will show below:

Answer 49

One of the earlier answers was: 2 / sqrt(x(3x+4))
= 2 / sqrt(x) * sqrt(3x+4)
(earlier I had combined two square roots into one single square root. but here they want it as two separate square roots so I am splitting them.)

= 2 / { x^(1/2) * (3x+4)^1/2 }
= 2 x^(-1/2) (3x+4)^(-1/2)

Answer 50

The answer they accepted and all the 4 answers above are the SAME. Just different forms.

It is like saying 1/2, 0.5, 50%, one-half, 2/4 are all the same but they are saying everything else is wrong but only 0.5 is correct.

When they don't explicitly state what form they want it in they should accept all forms that yield the same result.

Answer 51

I have to log off now. Bye.

Answer 52

Well thank you so much for your help

Answer 53

You are welcome. Glad it worked out in the end.