Solve a-5b/a^2+ab*(b^2-a^2)/10b-2a

$$\frac { a - 5 b } { a ^ { 2 } + a b } \times \frac { ( b ^ { 2 } - a ^ { 2 } ) } { 10 b - 2 a }$$

Evaluate

$$-\frac{b}{2a}+\frac{1}{2}$$

Short Solution Steps

Multiply \frac{a-5b}{a^{2}+ab} times \frac{b^{2}-a^{2}}{10b-2a} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a-5b\right)\left(b^{2}-a^{2}\right)}{\left(a^{2}+ab\right)\left(10b-2a\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(a+b\right)\left(a-5b\right)\left(-a+b\right)}{2a\left(a+b\right)\left(-a+5b\right)}$$

Extract the negative sign in a-5b.

$$\frac{-\left(a+b\right)\left(-a+b\right)\left(-a+5b\right)}{2a\left(a+b\right)\left(-a+5b\right)}$$

Cancel out \left(a+b\right)\left(-a+5b\right) in both numerator and denominator.

$$\frac{-\left(-a+b\right)}{2a}$$

Expand the expression.

$$\frac{a-b}{2a}$$

Expand

$$-\frac{b}{2a}+\frac{1}{2}$$

Short Solution Steps

Multiply \frac{a-5b}{a^{2}+ab} times \frac{b^{2}-a^{2}}{10b-2a} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a-5b\right)\left(b^{2}-a^{2}\right)}{\left(a^{2}+ab\right)\left(10b-2a\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(a+b\right)\left(a-5b\right)\left(-a+b\right)}{2a\left(a+b\right)\left(-a+5b\right)}$$

Extract the negative sign in a-5b.

$$\frac{-\left(a+b\right)\left(-a+b\right)\left(-a+5b\right)}{2a\left(a+b\right)\left(-a+5b\right)}$$

Cancel out \left(a+b\right)\left(-a+5b\right) in both numerator and denominator.

$$\frac{-\left(-a+b\right)}{2a}$$

Expand the expression.

$$\frac{a-b}{2a}$$