# Rational equations?

• December 11th 2010, 01:39 PM
homeylova223
Rational equations?
I am having difficulty solving this equation
solve the rational equation
(-4)/(x-1)=7/(2-x)+3/(x+1)
So far I got used the least common factor of 2 and (x-1)(x+1)
To get -8(x+1)=7(x+1)+6(x-1)
But the answer on the back of my book is 5/13 while I get like -9/21?I am confused.
• December 11th 2010, 01:47 PM
dwsmith
$\displaystyle \frac{-4}{(x-1)}*(x-1)=(x-1)\left[\frac{7}{2-x}+\frac{3}{x+1}\right]\Rightarrow-4=\cdots$
• December 11th 2010, 02:20 PM
Soroban
Hello, homeylova223!

Quote:

$\displaystyle \frac{-4}{x-1} \;=\; \frac{7}{2-x} + \frac{3}{x+1}$

I rewrote it like this:

. . $\displaystyle \frac{-4}{x-1} \;=\;\frac{-7}{x-2} + \frac{3}{x+1}$

Then the Least Common Denominator is: . $(x-1)(x-2)(x+1)$

Multply through by the LCD:

. . $-7(x-1)(x-2) \;=\; -3(x-1)(x+1) + 3(x-1)(x-2)$

. . . . $-4(x^2-x-2) \;=\;-7(x^2-1) + 3(x^2-3x+2)$

. . . . $-4x^2 + 4x + 8 \;=\;-7x^2 + 7 + 3x^2 - 9x + 6$

. . . . . . . . . . . . $13x \;=\;5$

. . . . . . . . . . . . . $x \;=\;\dfrac{5}{13}$