Solve frac{a^{2}-5a}{b-b^{2}}*b^2-1/a^2+6a-55*ab^2+11b^2/ax+3a

$$\frac { a ^ { 2 } - 5 a } { b - b ^ { 2 } } \times \frac { b ^ { 2 } - 1 } { a ^ { 2 } + 6 a - 55 } \times \frac { a b ^ { 2 } + 11 b ^ { 2 } } { a x + 3 a }$$

Evaluate

$$-\frac{b\left(b+1\right)}{x+3}$$

Short Solution Steps

Multiply \frac{a^{2}-5a}{b-b^{2}} times \frac{b^{2}-1}{a^{2}+6a-55} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a^{2}-5a\right)\left(b^{2}-1\right)}{\left(b-b^{2}\right)\left(a^{2}+6a-55\right)}\times \frac{ab^{2}+11b^{2}}{ax+3a}$$

Multiply \frac{\left(a^{2}-5a\right)\left(b^{2}-1\right)}{\left(b-b^{2}\right)\left(a^{2}+6a-55\right)} times \frac{ab^{2}+11b^{2}}{ax+3a} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a^{2}-5a\right)\left(b^{2}-1\right)\left(ab^{2}+11b^{2}\right)}{\left(b-b^{2}\right)\left(a^{2}+6a-55\right)\left(ax+3a\right)}$$

Factor the expressions that are not already factored.

$$\frac{a\left(a-5\right)\left(b-1\right)\left(a+11\right)\left(b+1\right)b^{2}}{ab\left(a-5\right)\left(a+11\right)\left(x+3\right)\left(-b+1\right)}$$

Extract the negative sign in -1+b.

$$\frac{-a\left(a-5\right)\left(a+11\right)\left(b+1\right)\left(-b+1\right)b^{2}}{ab\left(a-5\right)\left(a+11\right)\left(x+3\right)\left(-b+1\right)}$$

Cancel out ab\left(a-5\right)\left(a+11\right)\left(-b+1\right) in both numerator and denominator.

$$\frac{-b\left(b+1\right)}{x+3}$$

Expand the expression.

$$\frac{-b^{2}-b}{x+3}$$

Expand

$$-\frac{b^{2}+b}{x+3}$$

Short Solution Steps

Multiply \frac{a^{2}-5a}{b-b^{2}} times \frac{b^{2}-1}{a^{2}+6a-55} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a^{2}-5a\right)\left(b^{2}-1\right)}{\left(b-b^{2}\right)\left(a^{2}+6a-55\right)}\times \frac{ab^{2}+11b^{2}}{ax+3a}$$

Multiply \frac{\left(a^{2}-5a\right)\left(b^{2}-1\right)}{\left(b-b^{2}\right)\left(a^{2}+6a-55\right)} times \frac{ab^{2}+11b^{2}}{ax+3a} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a^{2}-5a\right)\left(b^{2}-1\right)\left(ab^{2}+11b^{2}\right)}{\left(b-b^{2}\right)\left(a^{2}+6a-55\right)\left(ax+3a\right)}$$

Factor the expressions that are not already factored.

$$\frac{a\left(a-5\right)\left(b-1\right)\left(a+11\right)\left(b+1\right)b^{2}}{ab\left(a-5\right)\left(a+11\right)\left(x+3\right)\left(-b+1\right)}$$

Extract the negative sign in -1+b.

$$\frac{-a\left(a-5\right)\left(a+11\right)\left(b+1\right)\left(-b+1\right)b^{2}}{ab\left(a-5\right)\left(a+11\right)\left(x+3\right)\left(-b+1\right)}$$

Cancel out ab\left(a-5\right)\left(a+11\right)\left(-b+1\right) in both numerator and denominator.

$$\frac{-b\left(b+1\right)}{x+3}$$

Expand the expression.

$$\frac{-b^{2}-b}{x+3}$$