Solve 2/7ab-3/14a^2b+4/21ab^2

$$\frac { 2 } { 7 a b } - \frac { 3 } { 14 a ^ { 2 } b } + \frac { 4 } { 21 a b ^ { 2 } }$$

Evaluate

$$\frac{12ab+8a-9b}{42\left(ab\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7ab and 14a^{2}b is 14ba^{2}. Multiply \frac{2}{7ab} times \frac{2a}{2a}.

$$\frac{2\times 2a}{14ba^{2}}-\frac{3}{14ba^{2}}+\frac{4}{21ab^{2}}$$

Since \frac{2\times 2a}{14ba^{2}} and \frac{3}{14ba^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times 2a-3}{14ba^{2}}+\frac{4}{21ab^{2}}$$

Do the multiplications in 2\times 2a-3.

$$\frac{4a-3}{14ba^{2}}+\frac{4}{21ab^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 14ba^{2} and 21ab^{2} is 42a^{2}b^{2}. Multiply \frac{4a-3}{14ba^{2}} times \frac{3b}{3b}. Multiply \frac{4}{21ab^{2}} times \frac{2a}{2a}.

$$\frac{\left(4a-3\right)\times 3b}{42a^{2}b^{2}}+\frac{4\times 2a}{42a^{2}b^{2}}$$

Since \frac{\left(4a-3\right)\times 3b}{42a^{2}b^{2}} and \frac{4\times 2a}{42a^{2}b^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(4a-3\right)\times 3b+4\times 2a}{42a^{2}b^{2}}$$

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

$$\frac{12ab-9b+8a}{42a^{2}b^{2}}$$

Factor

$$\frac{12ab+8a-9b}{42\left(ab\right)^{2}}$$