# Thread: solve for X with a rational

1. ## solve for X with a rational

This is an easy one I'm sure

x/a-1 = ax + 3

I tried taking out the (a-1) by multiplying both sides.
Then get stuck combining and isolating terms.

I know the final answer 3-3a/a^2-a-1 (in the back of the book)
I just can't get there.
Can someone show me the way.
Thx

2. Originally Posted by mathobust
This is an easy one I'm sure

x/a-1 = ax + 3

I tried taking out the (a-1) by multiplying both sides.
Then get stuck combining and isolating terms.

I know the final answer 3-3a/a^2-a-1 (in the back of the book)
I just can't get there.
Can someone show me the way.
Thx
i suppose you want to solve $\frac x{a - 1} = ax + 3$ ....(use parentheses)

multiply through by a - 1:

$\Rightarrow x = (a - 1)(ax + 3)$ .......................expand the right hand side:

$\Rightarrow x = a^2x + 3a - ax - 3$ ..................get all the x's on one side:

$\Rightarrow x - a^2x + ax = 3a - 3$ ...................factor out the x on the left hand side

$\Rightarrow x(1 - a^2 + a) = 3a - 3$ ..................divide both sides by the coefficient of x

$\Rightarrow x = \frac {3a - 3}{1 + a - a^2}$ ..............................multiply the right hand side by $\frac {-1}{-1}$

$\Rightarrow \boxed{x = \frac {3 - 3a}{a^2 - a - 1}}$

3. ## multiply the right hand side by -1/-1

Thanks for the quick response. Wish I would found this forum 2 days ago.

Question what triggers the multiply with -1/-1?

Question how can I get the correct fonts to show rationals, roots and exponents for my posts?

Thank you again.

4. Originally Posted by mathobust
Thanks for the quick response. Wish I would found this forum 2 days ago.

Question what triggers the multiply with -1/-1?
to get the answer in the exact form it was in the back of the book. we didn't have to do it, but students get weirded out by that sort of thing, when the answer is off by a factor of -1 in the numerator and denominator. a lot of people can't tell it's the same thing, so i sought to spare you from that. note that -1/-1 = 1. so what i did was multiply by one, so i really didn't change anything

Question how can I get the correct fonts to show rationals, roots and exponents for my posts?
go to our LaTeX forum, then see our LaTeX tutorial. LaTeX is the typesetting language we use to get the pretty math symbols here.

5. Originally Posted by mathobust
Thanks for the quick response. Wish I would found this forum 2 days ago.

Question what triggers the multiply with -1/-1?

Question how can I get the correct fonts to show rationals, roots and exponents for my posts?

Thank you again.
It is supposed to read "multiply through by (a - 1)"

-Dan