Solve a^2-6a+5/a^2-15a+5bdiva^2+2a-35/a^3-5a-24

$$\frac { a ^ { 2 } - 6 a + 5 } { a ^ { 2 } - 15 a + 5 b } \div \frac { a ^ { 2 } + 2 a - 35 } { a ^ { 3 } - 5 a - 24 }$$

Evaluate

$$\frac{\left(a-1\right)\left(a^{3}-5a-24\right)}{\left(a+7\right)\left(a^{2}-15a+5b\right)}$$

Short Solution Steps

Divide \frac{a^{2}-6a+5}{a^{2}-15a+5b} by \frac{a^{2}+2a-35}{a^{3}-5a-24} by multiplying \frac{a^{2}-6a+5}{a^{2}-15a+5b} by the reciprocal of \frac{a^{2}+2a-35}{a^{3}-5a-24}.

$$\frac{\left(a^{2}-6a+5\right)\left(a^{3}-5a-24\right)}{\left(a^{2}-15a+5b\right)\left(a^{2}+2a-35\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(a-5\right)\left(a-1\right)\left(a^{3}-5a-24\right)}{\left(a-5\right)\left(a+7\right)\left(a^{2}-15a+5b\right)}$$

Cancel out a-5 in both numerator and denominator.

$$\frac{\left(a-1\right)\left(a^{3}-5a-24\right)}{\left(a+7\right)\left(a^{2}-15a+5b\right)}$$

Expand the expression.

$$\frac{a^{4}-a^{3}-5a^{2}-19a+24}{a^{3}-8a^{2}+5ab-105a+35b}$$

Expand

$$\frac{a^{4}-a^{3}-5a^{2}-19a+24}{\left(a+7\right)\left(a^{2}-15a+5b\right)}$$

Short Solution Steps

Divide \frac{a^{2}-6a+5}{a^{2}-15a+5b} by \frac{a^{2}+2a-35}{a^{3}-5a-24} by multiplying \frac{a^{2}-6a+5}{a^{2}-15a+5b} by the reciprocal of \frac{a^{2}+2a-35}{a^{3}-5a-24}.

$$\frac{\left(a^{2}-6a+5\right)\left(a^{3}-5a-24\right)}{\left(a^{2}-15a+5b\right)\left(a^{2}+2a-35\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(a-5\right)\left(a-1\right)\left(a^{3}-5a-24\right)}{\left(a-5\right)\left(a+7\right)\left(a^{2}-15a+5b\right)}$$

Cancel out a-5 in both numerator and denominator.

$$\frac{\left(a-1\right)\left(a^{3}-5a-24\right)}{\left(a+7\right)\left(a^{2}-15a+5b\right)}$$

Expand the expression.

$$\frac{a^{4}-a^{3}-5a^{2}-19a+24}{a^{3}-8a^{2}+5ab-105a+35b}$$