Solve sqrt{a^2+ab/a+b}=sqrt{a(a+b)/a+b}

$$\sqrt { \frac { a ^ { 2 } + a b } { a + b } } = \sqrt { \frac { a ( a + b ) } { a + b } }$$

Solve for a (complex solution)

$$a\neq -b$$

Short Solution Steps

Use the distributive property to multiply a by a+b.

$$\sqrt{\frac{a^{2}+ab}{a+b}}=\sqrt{\frac{a^{2}+ab}{a+b}}$$

Reorder the terms.

$$\text{true}$$

This is true for any a.

$$a\in \mathrm{C}$$

Solve for b (complex solution)

$$b\neq -a$$

Short Solution Steps

Use the distributive property to multiply a by a+b.

$$\sqrt{\frac{a^{2}+ab}{a+b}}=\sqrt{\frac{a^{2}+ab}{a+b}}$$

Reorder the terms.

$$\text{true}$$

This is true for any b.

$$b\in \mathrm{C}$$

Solve for a

$$\left\{\begin{matrix}a\geq 0\text{, }&b>0\\a\in [0,-b)\cup (-b,\infty)\text{, }&b\leq 0\end{matrix}\right.$$

Short Solution Steps

Use the distributive property to multiply a by a+b.

$$\sqrt{\frac{a^{2}+ab}{a+b}}=\sqrt{\frac{a^{2}+ab}{a+b}}$$

Reorder the terms.

$$\text{true}$$

This is true for any a.

$$a\in \mathrm{R}$$

Solve for b

$$b\neq -a$$

$$a\geq 0$$

Short Solution Steps

Use the distributive property to multiply a by a+b.

$$\sqrt{\frac{a^{2}+ab}{a+b}}=\sqrt{\frac{a^{2}+ab}{a+b}}$$

Reorder the terms.

$$\text{true}$$

This is true for any b.

$$b\in \mathrm{R}$$