Question

Solve: (x/(x-3))+ (9/(x+1))=4

Answer 1

\[\frac{x}{x-3}+\frac{9}{x+1}=\frac{x(x+1)+9(x-3)}{(x-3)(x+1)}\] is a start

Answer 2

you get
\[\frac{x^2+x+9x-27}{(x-3)(x+1)}=\frac{x^2+10x-27}{(x-3)(x+1)}=4\]

Answer 3

so
\[x^2+10x-27=4(x-3)(x+1)\] and so multiply out and get a quadratic equation (which actually factors)
you good from there?

Answer 4

Yes, I believe so. Thanks again. You're a lifesaver.

Answer 5

x/(x-3)+9/(x+1)=4 Multiply by x-3 to eliminate the denominator x-3

x+(9)(x-3)/(x+1)=4(x-3) Multiply by x+1 to eliminate the denominator x+1

x(x+1)+9(x-#)=4(x-3)(x+1)

x^2+x+9x-27=4(x^2-2x-3)

x^2+10x-27=4x^-8x-12

4x^2-8x-12-x^2-10x+27=0

3x^-18x+15=0

(3x-3)(x-5)=0

3x-3=0
3x=3
x=1

x-5=0
x=5

Therefore, x=1 and x=5

Answer 6

Yes, I believe so. Thanks again. You're a lifesaver.