Question

Solve this equation

(Question will be posted below)

Answer 1

\[\large \frac{ 1 }{ x } = 3 + \frac{7}{x^2+7x}\]

Answer 2

x can not be 0,-7

Answer 3

calculusxy: Please identify the LCD of these 3 terms.

Next, mult. each term by this LCD, to eliminate fractions.

Answer 4

Yes because \(x^2 + 7x\) is (in factored form) \((x-7)(x-0)\)

Answer 5

now take lcm and solve but x not 0 and -7

Answer 6

@mathmale I thought that the LCD can be \(x^2 + 7x\). So I would have
\(\huge \frac{x^2+7x}{x^2+7x} = \frac{3x^2+21x+7}{x^2+7x}\)
it would be basically
\(\huge \frac{x^2 + 7x + 3x^2 + 21x + 7}{x^2+7x}\ = \frac{4x^2+28x+7}{x^2+7x}\)

Answer 7

Am I correct? If I am, how can I factor \(4x^2 + 28x+7\)?

Answer 8

No

Answer 9

May I know how?

Answer 10

x(x^2+7x) is the LCD, yes.

Multiply each term by this x(x^2+7x) and then cancel, where possible, in each case.

Answer 11

where is x of 1/x go?

Answer 12

I multiplied it with \(x^2 +7x\).

Answer 13

\[\frac{ x(x+7) }{ x }=?\]

Answer 14

Okay give me moment as I am redoing the problem.

Answer 15

\[x(x+7)*3=?\]

Answer 16

\[\frac{ x(x+7)(7) }{ x^2+7x }+?\]

Answer 17

x(x+7)/x=?

Answer 18

just cross multiply and solve it

Answer 19

So I what have is
\(\huge\frac{1(x+7) = 3x(x+7) + 7}{x(x+7)}\)

Answer 20

yes

Answer 21

Yes, and now you can throw out the common denominator.

Answer 22

solve the equation in your numerator.

Answer 23

ok
\(x+7=3x(x+7) + 7\)
\(x+7 = 3x^2 + 21x + 7\)
\(3x^2 + 20x + 0\)

Answer 24

would this quadratic be correct?

Answer 25

Yes, I believe so. What are the roots of that?

Answer 26

If I try to solve for it with the quadratic formula I get
\(\large \frac{-20 \pm \sqrt{400}}{6}\)

\(\large \frac{-20\pm20}{6}\)

\(\large x = (0, -\frac{20}{3})\)

Answer 27

I think the answer would be \(\large -\frac{20}{3}\)

Answer 28

Because 0 is the extraneous solution

Answer 29

Now we'll need to check both of those possible solutions in the original equation. Yes, 0 is extraneous because we cannot divide by zero.

Next step?

Answer 30

x=-20/3 is correct.

Answer 31

I think that you can plug it back into the original equation and check if it works out. But I needed help to get to this far. Thank you much for the help @mathmale and @Er.Mohd.AMIR !

Answer 32

You're welcome!