Quick solve for X type fraction question.

[nukeman]

Homework Statement

2 = x+2 over x-6

Homework Equations

The Attempt at a Solution

So, multiply both sides by 2 right?

For some reason I am not getting what my book says is right. The end answer is x = 14

I must be doing a step wrong. Can someone show me the steps involved here?

Thanks :)

 

[fss]

The Attempt at a Solution

So, multiply both sides by 2 right?

How would that help you? What could you multiply by on both sides to get rid of that fraction?

 

[QuarkCharmer]

2=(x+2)/(x-6)

Maybe it would help if you think of each as a variable. So consider

T = M/N

How would you go about moving N to the T side to eliminate the fraction? You would multiply it both sides of the equation so that:
NT = MN/N canceling out the right N's leaving:
NT = M

Consider the expressions in the parenthesis as it's own little group.

 

[HallsofIvy]

Homework Statement

2 = x+2 over x-6

Homework Equations

The Attempt at a Solution

So, multiply both sides by 2 right?

No, I can't imagine why you would think that.

For some reason I am not getting what my book says is right. The end answer is x = 14

I must be doing a step wrong. Can someone show me the steps involved here?

Thanks :)

Well if x= 14, then x+ 2= 16 and x- 2= 12. 16/12= 8/3, not 2. Where did you get x= 14 as the answer?

 

[Mark44]

No, I can't imagine why you would think that.


Well if x= 14, then x+ 2= 16 and x- 2= 12. 16/12= 8/3, not 2. Where did you get x= 14 as the answer?

The denominator is x - 6, not x - 2. If x = 14, the numerator is 16, and the denominator is 8, so when x = 14, (x + 2)/(x - 6) = 2.

 

[SammyS]

Here's a weird way to solve it.$$\frac{x+2}{x-6}=\frac{x-6+6+2}{x-6}=\frac{x-6}{x-6}+\frac{8}{x-6}=1+\frac{8}{x-6}$$

 

[nukeman]

Ok, let's do this one. Can someone please help with this?

If f(x) = 2, solve for x

x+1 over x+2

The right answer is x = -3 I am not sure how to get -3 from that??

Thanks so much guys!

 

[eumyang]

We can't just tell you. You have to try it yourself first. Have you read QuarkCharmer's post above? It shows you the first step you need to take.