What is 1/(y-2)+2/(y+1)-(y+2)/(y^2-y-2) ?

The solution to 1/(y-2)+2/(y+1)-(y+2)/(y^2-y-2) is (2y-5)/((y-2)(y+1))

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simplify 1/(y-2)+2/(y+1)-(y+2)/(y^2-y-2)

simplify

\frac{1}{y - 2} + \frac{2}{y + 1} - \frac{y + 2}{y ^{2} - y - 2}

\frac{2 y - 5}{( y - 2 ) ( y + 1 )}

Solution steps

\frac{1}{y - 2} + \frac{2}{y + 1} - \frac{y + 2}{y ^{2} - y - 2}

Least Common Multiplier of

y - 2, y + 1, y^{2} - y - 2 : (y - 2) (y + 1)

Adjust Fractions based on the LCM

= \frac{y + 1}{( y - 2 ) ( y + 1 )} + \frac{2 ( y - 2 )}{( y - 2 ) ( y + 1 )} - \frac{y + 2}{( y - 2 ) ( y + 1 )}

Apply the fraction rule:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{y + 1 + 2 ( y - 2 ) - ( y + 2 )}{( y - 2 ) ( y + 1 )}

Simplify

y + 1 + 2 (y - 2) - (y + 2) : 2 y - 5

= \frac{2 y - 5}{( y - 2 ) ( y + 1 )}

\frac{1}{7} + \frac{5}{5}

\frac{x ^{2} - 16}{x ^{2} + 4 x}

\frac{9 + 13 i}{- 4 - 3 i}

100 \div 10

(x - 2) (x - 8)

What is 1/(y-2)+2/(y+1)-(y+2)/(y^2-y-2) ?
The solution to 1/(y-2)+2/(y+1)-(y+2)/(y^2-y-2) is (2y-5)/((y-2)(y+1))