Solve a^2+2a+1/adiva^2/a^2-1

$$\frac { a ^ { 2 } + 2 a + 1 } { a } \div \frac { a ^ { 2 } } { a ^ { 2 } - 1 }$$

Evaluate

$$\left(\frac{a+1}{a}\right)^{3}\left(a-1\right)$$

Short Solution Steps

Divide \frac{a^{2}+2a+1}{a} by \frac{a^{2}}{a^{2}-1} by multiplying \frac{a^{2}+2a+1}{a} by the reciprocal of \frac{a^{2}}{a^{2}-1}.

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

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

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

Use the distributive property to multiply a^{2}+2a+1 by a^{2}-1 and combine like terms.

$$\frac{a^{4}+2a^{3}-2a-1}{a^{3}}$$

Expand

$$a+2-\frac{2}{a^{2}}-\frac{1}{a^{3}}$$

Short Solution Steps

Divide \frac{a^{2}+2a+1}{a} by \frac{a^{2}}{a^{2}-1} by multiplying \frac{a^{2}+2a+1}{a} by the reciprocal of \frac{a^{2}}{a^{2}-1}.

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

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

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

Use the distributive property to multiply a^{2}+2a+1 by a^{2}-1 and combine like terms.

$$\frac{a^{4}+2a^{3}-2a-1}{a^{3}}$$