Solve (1/a+1/b)*1/ab(a+b)

$$( \frac { 1 } { a } + \frac { 1 } { b } ) \times \frac { 1 } { a b ( a + b ) }$$

Evaluate

$$\frac{1}{\left(ab\right)^{2}}$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a and b is ab. Multiply \frac{1}{a} times \frac{b}{b}. Multiply \frac{1}{b} times \frac{a}{a}.

$$\left(\frac{b}{ab}+\frac{a}{ab}\right)\times \frac{1}{ab\left(a+b\right)}$$

Since \frac{b}{ab} and \frac{a}{ab} have the same denominator, add them by adding their numerators.

$$\frac{b+a}{ab}\times \frac{1}{ab\left(a+b\right)}$$

Multiply \frac{b+a}{ab} times \frac{1}{ab\left(a+b\right)} by multiplying numerator times numerator and denominator times denominator.

$$\frac{b+a}{abab\left(a+b\right)}$$

Cancel out a+b in both numerator and denominator.

$$\frac{1}{aabb}$$

Multiply a and a to get a^{2}.

$$\frac{1}{a^{2}bb}$$

Multiply b and b to get b^{2}.

$$\frac{1}{a^{2}b^{2}}$$

Expand

$$\frac{1}{\left(ab\right)^{2}}$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a and b is ab. Multiply \frac{1}{a} times \frac{b}{b}. Multiply \frac{1}{b} times \frac{a}{a}.

$$\left(\frac{b}{ab}+\frac{a}{ab}\right)\times \frac{1}{ab\left(a+b\right)}$$

Since \frac{b}{ab} and \frac{a}{ab} have the same denominator, add them by adding their numerators.

$$\frac{b+a}{ab}\times \frac{1}{ab\left(a+b\right)}$$

Multiply \frac{b+a}{ab} times \frac{1}{ab\left(a+b\right)} by multiplying numerator times numerator and denominator times denominator.

$$\frac{b+a}{abab\left(a+b\right)}$$

Cancel out a+b in both numerator and denominator.

$$\frac{1}{aabb}$$

Multiply a and a to get a^{2}.

$$\frac{1}{a^{2}bb}$$

Multiply b and b to get b^{2}.

$$\frac{1}{a^{2}b^{2}}$$