Solve a^2+7a/a^2+1*a+7/a+1=

$$\frac { a ^ { 2 } + 7 a } { a ^ { 2 } + 1 } \cdot \frac { a + 7 } { a + 1 } =$$

Evaluate

$$\frac{a\left(a+7\right)^{2}}{\left(a+1\right)\left(a^{2}+1\right)}$$

Short Solution Steps

Multiply \frac{a^{2}+7a}{a^{2}+1} times \frac{a+7}{a+1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a^{2}+7a\right)\left(a+7\right)}{\left(a^{2}+1\right)\left(a+1\right)}$$

Use the distributive property to multiply a^{2}+7a by a+7 and combine like terms.

$$\frac{a^{3}+14a^{2}+49a}{\left(a^{2}+1\right)\left(a+1\right)}$$

Use the distributive property to multiply a^{2}+1 by a+1.

$$\frac{a^{3}+14a^{2}+49a}{a^{3}+a^{2}+a+1}$$

Expand

$$\frac{a^{3}+14a^{2}+49a}{\left(a+1\right)\left(a^{2}+1\right)}$$

Short Solution Steps

Multiply \frac{a^{2}+7a}{a^{2}+1} times \frac{a+7}{a+1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a^{2}+7a\right)\left(a+7\right)}{\left(a^{2}+1\right)\left(a+1\right)}$$

Use the distributive property to multiply a^{2}+7a by a+7 and combine like terms.

$$\frac{a^{3}+14a^{2}+49a}{\left(a^{2}+1\right)\left(a+1\right)}$$

Use the distributive property to multiply a^{2}+1 by a+1.

$$\frac{a^{3}+14a^{2}+49a}{a^{3}+a^{2}+a+1}$$