Solve 1/a^2+3/b^2=

$$\frac { 1 } { a ^ { 2 } } + \frac { 3 } { b ^ { 2 } } =$$

Evaluate

$$\frac{3a^{2}+b^{2}}{\left(ab\right)^{2}}$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a^{2} and b^{2} is a^{2}b^{2}. Multiply \frac{1}{a^{2}} times \frac{b^{2}}{b^{2}}. Multiply \frac{3}{b^{2}} times \frac{a^{2}}{a^{2}}.

$$\frac{b^{2}}{a^{2}b^{2}}+\frac{3a^{2}}{a^{2}b^{2}}$$

Since \frac{b^{2}}{a^{2}b^{2}} and \frac{3a^{2}}{a^{2}b^{2}} have the same denominator, add them by adding their numerators.

$$\frac{b^{2}+3a^{2}}{a^{2}b^{2}}$$

Factor

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