Solve 2/a^2-3/ab+4/b^2

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

Evaluate

$$\frac{4a^{2}-3ab+2b^{2}}{\left(ab\right)^{2}}$$

Short Solution Steps

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

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of ba^{2} and b^{2} is a^{2}b^{2}. Multiply \frac{2b-3a}{ba^{2}} times \frac{b}{b}. Multiply \frac{4}{b^{2}} times \frac{a^{2}}{a^{2}}.

$$\frac{\left(2b-3a\right)b}{a^{2}b^{2}}+\frac{4a^{2}}{a^{2}b^{2}}$$

Since \frac{\left(2b-3a\right)b}{a^{2}b^{2}} and \frac{4a^{2}}{a^{2}b^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(2b-3a\right)b+4a^{2}}{a^{2}b^{2}}$$

Do the multiplications in \left(2b-3a\right)b+4a^{2}.

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

Factor

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