What is 2/(p^2+pq)+3/(pq-q^2) ?

The solution to 2/(p^2+pq)+3/(pq-q^2) is (-2q^2+3p^2+5pq)/((p^2+pq)(-q^2+pq))

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simplify 2/(p^2+pq)+3/(pq-q^2)

simplify

\frac{2}{p ^{2} + pq} + \frac{3}{pq - q ^{2}}

\frac{- 2 q ^{2} + 3 p ^{2} + 5 pq}{( p ^{2} + pq ) ( - q ^{2} + pq )}

Solution steps

\frac{2}{p ^{2} + pq} + \frac{3}{pq - q ^{2}}

Least Common Multiplier of

p^{2} + pq, pq - q^{2} : (p^{2} + pq) (- q^{2} + pq)

Adjust Fractions based on the LCM

= \frac{2 ( - q ^{2} + pq )}{( p ^{2} + pq ) ( - q ^{2} + pq )} + \frac{3 ( p ^{2} + pq )}{( p ^{2} + pq ) ( - q ^{2} + pq )}

Apply the fraction rule:

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

= \frac{2 ( - q ^{2} + pq ) + 3 ( p ^{2} + pq )}{( p ^{2} + pq ) ( - q ^{2} + pq )}

Simplify

2 (- q^{2} + pq) + 3 (p^{2} + pq) : - 2 q^{2} + 3 p^{2} + 5 pq

= \frac{- 2 q ^{2} + 3 p ^{2} + 5 pq}{( p ^{2} + pq ) ( - q ^{2} + pq )}

\frac{2}{x} \frac{5}{y}

3 r^{2} + 8 r + 5

3 X - 5 < \frac{3}{4} X + \frac{( 1 - X )}{3}

- 0.5 x^{2} + 2 x + 11 = - x + 3

e^{2 + 4 i}

What is 2/(p^2+pq)+3/(pq-q^2) ?
The solution to 2/(p^2+pq)+3/(pq-q^2) is (-2q^2+3p^2+5pq)/((p^2+pq)(-q^2+pq))