Solve a(a+5)(a-5)(a+4/a^2-5a)

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

Evaluate

$$\left(a+4\right)\left(a+5\right)$$

Short Solution Steps

Express a\times \frac{a+4}{a^{2}-5a} as a single fraction.

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

Use the distributive property to multiply \frac{a\left(a+4\right)}{a^{2}-5a} by a+5.

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

Factor the expressions that are not already factored in \frac{a\left(a+4\right)}{a^{2}-5a}.

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

Cancel out a in both numerator and denominator.

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

Express \frac{a+4}{a-5}a as a single fraction.

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

Factor the expressions that are not already factored in \frac{a\left(a+4\right)}{a^{2}-5a}.

$$\left(\frac{\left(a+4\right)a}{a-5}+5\times \frac{a\left(a+4\right)}{a\left(a-5\right)}\right)\left(a-5\right)$$

Cancel out a in both numerator and denominator.

$$\left(\frac{\left(a+4\right)a}{a-5}+5\times \frac{a+4}{a-5}\right)\left(a-5\right)$$

Express 5\times \frac{a+4}{a-5} as a single fraction.

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

Since \frac{\left(a+4\right)a}{a-5} and \frac{5\left(a+4\right)}{a-5} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(a+4\right)a+5\left(a+4\right).

$$\frac{a^{2}+4a+5a+20}{a-5}\left(a-5\right)$$

Combine like terms in a^{2}+4a+5a+20.

$$\frac{a^{2}+9a+20}{a-5}\left(a-5\right)$$

Cancel out a-5 and a-5.

$$a^{2}+9a+20$$

Expand

$$a^{2}+9a+20$$

Short Solution Steps

Express a\times \frac{a+4}{a^{2}-5a} as a single fraction.

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

Use the distributive property to multiply \frac{a\left(a+4\right)}{a^{2}-5a} by a+5.

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

Factor the expressions that are not already factored in \frac{a\left(a+4\right)}{a^{2}-5a}.

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

Cancel out a in both numerator and denominator.

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

Express \frac{a+4}{a-5}a as a single fraction.

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

Factor the expressions that are not already factored in \frac{a\left(a+4\right)}{a^{2}-5a}.

$$\left(\frac{\left(a+4\right)a}{a-5}+5\times \frac{a\left(a+4\right)}{a\left(a-5\right)}\right)\left(a-5\right)$$

Cancel out a in both numerator and denominator.

$$\left(\frac{\left(a+4\right)a}{a-5}+5\times \frac{a+4}{a-5}\right)\left(a-5\right)$$

Express 5\times \frac{a+4}{a-5} as a single fraction.

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

Since \frac{\left(a+4\right)a}{a-5} and \frac{5\left(a+4\right)}{a-5} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(a+4\right)a+5\left(a+4\right).

$$\frac{a^{2}+4a+5a+20}{a-5}\left(a-5\right)$$

Combine like terms in a^{2}+4a+5a+20.

$$\frac{a^{2}+9a+20}{a-5}\left(a-5\right)$$

Cancel out a-5 and a-5.

$$a^{2}+9a+20$$