Question

Solve the following equation:
3x+1/3x+2 = x+2/x-5

A. -9/22
B. -9/23
C. -3/8
Please and thanks!!

Answer 1

\[\frac{3x + 1}{3x + 2} = \frac{x + 2}{x - 5}\]
\[\frac{3x + 2 - 1}{3x + 2} = \frac{x - 5 + 7}{x - 5}\]
\[\frac{3x + 2}{3x + 2} - \frac{1}{3x + 2}= \frac{x - 5}{x - 5} + \frac{7}{x - 5}\]
\[1 - \frac{1}{3x + 2}= 1 + \frac{7}{x - 5}\]
\[ - \frac{1}{3x + 2}= \frac{7}{x - 5}\]
\[-1(x - 5) = 7(3x + 2)\]
\[5 - x = 21x + 14\]
\[-(14 - 5) = (21 + 1)x\]
\[-9 = 22x\]
\[-\frac{9}{22} = x\]