Question

Can anyone help with these two last questions of my homework because I don't understand!!?
Solve for x.....

2. (1/2) + (4/2x) = (x+4/10)

9. (5/x^2-4) + (2/x) = (2/x-2)

Answer 1

do you know how to get rid of the fractions here?

Answer 2

no i don't. I don't know how to add fractions at all...stupid isn't!!

Answer 3

don't put yourself down - I'm sure you are capable of learning. we've all been there :-)

Answer 4

ok, first let me confirm the equation....

Answer 5

is the first one:\[\frac{1}{2}+\frac{4}{2x}=\frac{x+4}{10}\]

Answer 6

yes

Answer 7

ok - now what you need to do is see what to multiply both sides by in order to get rid of the fractions.
we can do this one step at a time so that you can understand the process.

Answer 8

by 2 !?!

Answer 9

so 1st I see a 2 in the denominator of the first fraction on the left, so lets multiply both sides by 2 to get:

Answer 10

yes - you DO understand! :-)

Answer 11

multiplying by 2 we get:\[2*\frac{1}{2}+2*\frac{4}{2x}=2*\frac{x+4}{10}\]

Answer 12

but don't you want the denominators the same. wouldn't you multiply by 2x

Answer 13

now we cancel out common factors to get:\[\cancel{2}*\frac{1}{\cancel{2}}+\cancel{2}*\frac{4}{\cancel{2}x}=\cancel{2}*\frac{x+4}{\cancel{10}5}\]

Answer 14

I wanted to show you one step at a time, but if you are more confident, then we can go faster?

Answer 15

no its okay i was just curious

Answer 16

ok, so we end up with:\[1+\frac{4}{x}=\frac{x+4}{5}\]

Answer 17

next, as you spotted already, we can multiply both sides by x to get:\[x+4=\frac{x(x+4)}{5}\]

Answer 18

finally, we multiply both sides by 5 to get rid of the final fraction to get:\[5x+20=x(x+4)\]

Answer 19

so now we are left with a quadratic equation. do you know how to solve from here?

Answer 20

yes two questions though....
1. why did you multiply both side by x?
2. in the quadratic formula would it x^2 or 2x?

Answer 21

ok, when we got to this step above:\[1+\frac{4}{x}=\frac{x+4}{5}\]I noticed that we still have a fraction on the left hand side, and that this fraction has an "x" in the denominator. so we multiply both sides by "x" to get rid of this denominator.

Answer 22

and that canceled out the 1?

Answer 23

not cancelled out - 1 times "x" is equal to "x"

Answer 24

ohh okay

Answer 25

secondly, quadratic equations involve \(x^2\). so the final equation we got was:\[5x+20=x(x+4)\]which expands to:\[5x+20=x^2+4x\]and finally to:\[x^2-x-20=0\]

Answer 26

thank you!!!!!

Answer 27

hopefully you can do the 2nd equation yourself.
do you want to try it out yourself now and show me your steps?

Answer 28

ill try it out but im late for work so i have to go
thank you a lot though . it makes a lot more since to me know.

Answer 29

np - I'm glad I was able to explain it clearly enough for you to understand.