Solve (2)-4/a^2-3a^2-10*a^2+a-2/2a^2+10a

$$\frac { ( 2 ) - 4 } { a ^ { 2 } - 3 a ^ { 2 } - 10 } \cdot \frac { a ^ { 2 } + a - 2 } { 2 a ^ { 2 } + 10 a }$$

Evaluate

$$\frac{\left(a-1\right)\left(a+2\right)}{2a\left(a+5\right)\left(a^{2}+5\right)}$$

Short Solution Steps

Subtract 4 from 2 to get -2.

$$\frac{-2}{a^{2}-3a^{2}-10}\times \frac{a^{2}+a-2}{2a^{2}+10a}$$

Combine a^{2} and -3a^{2} to get -2a^{2}.

$$\frac{-2}{-2a^{2}-10}\times \frac{a^{2}+a-2}{2a^{2}+10a}$$

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

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

Use the distributive property to multiply -2 by a^{2}+a-2.

$$\frac{-2a^{2}-2a+4}{\left(-2a^{2}-10\right)\left(2a^{2}+10a\right)}$$

Use the distributive property to multiply -2a^{2}-10 by 2a^{2}+10a.

$$\frac{-2a^{2}-2a+4}{-4a^{4}-20a^{3}-20a^{2}-100a}$$

Factor the expressions that are not already factored.

$$\frac{2\left(a+2\right)\left(-a+1\right)}{4a\left(-a-5\right)\left(a^{2}+5\right)}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\left(a+2\right)\left(-a+1\right)}{2a\left(-a-5\right)\left(a^{2}+5\right)}$$

Expand the expression.

$$\frac{-a^{2}-a+2}{-2a^{4}-10a^{3}-10a^{2}-50a}$$

Expand

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

Short Solution Steps

Subtract 4 from 2 to get -2.

$$\frac{-2}{a^{2}-3a^{2}-10}\times \frac{a^{2}+a-2}{2a^{2}+10a}$$

Combine a^{2} and -3a^{2} to get -2a^{2}.

$$\frac{-2}{-2a^{2}-10}\times \frac{a^{2}+a-2}{2a^{2}+10a}$$

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

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

Use the distributive property to multiply -2 by a^{2}+a-2.

$$\frac{-2a^{2}-2a+4}{\left(-2a^{2}-10\right)\left(2a^{2}+10a\right)}$$

Use the distributive property to multiply -2a^{2}-10 by 2a^{2}+10a.

$$\frac{-2a^{2}-2a+4}{-4a^{4}-20a^{3}-20a^{2}-100a}$$

Factor the expressions that are not already factored.

$$\frac{2\left(a+2\right)\left(-a+1\right)}{4a\left(-a-5\right)\left(a^{2}+5\right)}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\left(a+2\right)\left(-a+1\right)}{2a\left(-a-5\right)\left(a^{2}+5\right)}$$

Expand the expression.

$$\frac{-a^{2}-a+2}{-2a^{4}-10a^{3}-10a^{2}-50a}$$