Answer:
Step-by-step explanation:
Begin by finding a common denominator in the numerator of that rational expression. The common denominator is 3(x+2):
[tex]\frac{\frac{(3)1}{(3)x+2} -\frac{(x+2)1}{3(x+2)} }{x-1}[/tex] which simplifies to
[tex]\frac{\frac{3}{3x+6} -\frac{(x+2)}{3x+6} }{x-1}[/tex] which simplifies further to
[tex]\frac{\frac{3-x-2}{3x+6} }{x-1}[/tex] and
[tex]\frac{\frac{1-x}{3x+6} }{x-1}[/tex] Bring up the lower fraction and flip it and multiply:
[tex]\frac{1-x}{3x+6}*\frac{1}{x-1}[/tex] In order to make the 1-x into x-1, multiply the numerator of that fraction on the left by -1 to get:
[tex]-\frac{x-1}{(3x+6)(x-1)}[/tex] and now the x-1 terms cancel out, leaving us with:
[tex]-\frac{1}{3(1)+6}=-\frac{1}{9}=-.1111[/tex]
