Question

Find all real solutions of the equation. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.)
1
x − 1
+
1
x + 5
=
8
7

Answer 1

1/(x-1) + 1/(x+5)= 8/7

Answer 2

\[\frac{1}{x-1}+\frac{1}{x+5} = \frac{8}{7}\]
\[\frac{x+5}{x+5}*\frac{1}{x-1}+\frac{x-1}{x-1}*\frac{1}{x+5} = \frac{8}{7}\]
\[\frac{(x+5)+(x-1)}{(x+5)(x-1)}= \frac{8}{7}\]
\[7(2x+4) = 8(x+5)(x-1)\]
\[7(2x+4) = 8(x^{2}+4x-5)\]
\[14x + 28 = 8x^{2}+32x -40\]
\[8x^{2}+18x -68 = 0\]
\[4x^{2}+9x-34 =0\]
\[4x^{2}-8x+17x-34 = 0\]
\[4x(x-2)+17(x-2) =0\]
\[(4x+17)(x-2) = 0\]
\[x = 2 , x = -17/4\]