Resolve into partial functions: (1+x)/((1-x)(2+x))

Question

ScanSolve AI Tutor · Accepted Answer

Here's the solution for problem 'b':

To subtract the fractions, find a common denominator.

Find the common denominator.
The common denominator for $\frac{4}{2x+3}$ and $\frac{1}{x-2}$ is the product of their denominators, which is $(2x+3)(x-2)$ .
Rewrite each fraction with the common denominator.
$\frac{4}{2x+3} = \frac{4(x-2)}{(2x+3)(x-2)}$ $\frac{1}{x-2} = \frac{1(2x+3)}{(2x+3)(x-2)}$
Subtract the fractions.
$\frac{4(x-2)}{(2x+3)(x-2)} - \frac{1(2x+3)}{(2x+3)(x-2)} = \frac{4(x-2) - (2x+3)}{(2x+3)(x-2)}$
Expand the numerator.
$4(x-2) - (2x+3) = 4x - 8 - 2x - 3$
Combine like terms in the numerator.
$4x - 2x - 8 - 3 = 2x - 11$
Write the final simplified expression.
$\frac{2x - 11}{(2x+3)(x-2)}$

Answer