Split the second term in \(5{x}^{2}+3x-2\) into two terms.
Multiply the coefficient of the first term by the constant term.
\[5\times -2=-10\]
Ask: Which two numbers add up to \(3\) and multiply to \(-10\)?
Split \(3x\) as the sum of \(5x\) and \(-2x\).
\[5{x}^{2}+5x-2x-2\]
\[\frac{7}{5{x}^{2}+5x-2x-2}-\frac{5}{5x-2}\]
Factor out common terms in the first two terms, then in the last two terms.
\[\frac{7}{5x(x+1)-2(x+1)}-\frac{5}{5x-2}\]
Factor out the common term \(x+1\).
\[\frac{7}{(x+1)(5x-2)}-\frac{5}{5x-2}\]
Rewrite the expression with a common denominator.
\[\frac{7-5(x+1)}{(x+1)(5x-2)}\]
Expand.
\[\frac{7-5x-5}{(x+1)(5x-2)}\]
Simplify \(7-5x-5\) to \(-5x+2\).
\[\frac{-5x+2}{(x+1)(5x-2)}\]
Factor out the negative sign in \(-5x+2\).
\[-\frac{5x-2}{(x+1)(5x-2)}\]
Cancel \(5x-2\).
\[-\frac{1}{x+1}\]
-1/(x+1)
