Solve 2/w-9/w^2/frac{2{w}+7/w^2}

$$\frac { \frac { 2 } { w } - \frac { 9 } { w ^ { 2 } } } { \frac { 2 } { w } + \frac { 7 } { w ^ { 2 } } }$$

Evaluate

$$\frac{2w-9}{2w+7}$$

Solution Steps

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

$$\frac{\frac{2w}{w^{2}}-\frac{9}{w^{2}}}{\frac{2}{w}+\frac{7}{w^{2}}}$$

Since \frac{2w}{w^{2}} and \frac{9}{w^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2w-9}{w^{2}}}{\frac{2}{w}+\frac{7}{w^{2}}}$$

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

$$\frac{\frac{2w-9}{w^{2}}}{\frac{2w}{w^{2}}+\frac{7}{w^{2}}}$$

Since \frac{2w}{w^{2}} and \frac{7}{w^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2w-9}{w^{2}}}{\frac{2w+7}{w^{2}}}$$

Divide \frac{2w-9}{w^{2}} by \frac{2w+7}{w^{2}} by multiplying \frac{2w-9}{w^{2}} by the reciprocal of \frac{2w+7}{w^{2}}.

$$\frac{\left(2w-9\right)w^{2}}{w^{2}\left(2w+7\right)}$$

Cancel out w^{2} in both numerator and denominator.

$$\frac{2w-9}{2w+7}$$

Expand

$$\frac{2w-9}{2w+7}$$

Solution Steps

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

$$\frac{\frac{2w}{w^{2}}-\frac{9}{w^{2}}}{\frac{2}{w}+\frac{7}{w^{2}}}$$

Since \frac{2w}{w^{2}} and \frac{9}{w^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2w-9}{w^{2}}}{\frac{2}{w}+\frac{7}{w^{2}}}$$

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

$$\frac{\frac{2w-9}{w^{2}}}{\frac{2w}{w^{2}}+\frac{7}{w^{2}}}$$

Since \frac{2w}{w^{2}} and \frac{7}{w^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2w-9}{w^{2}}}{\frac{2w+7}{w^{2}}}$$

Divide \frac{2w-9}{w^{2}} by \frac{2w+7}{w^{2}} by multiplying \frac{2w-9}{w^{2}} by the reciprocal of \frac{2w+7}{w^{2}}.

$$\frac{\left(2w-9\right)w^{2}}{w^{2}\left(2w+7\right)}$$

Cancel out w^{2} in both numerator and denominator.

$$\frac{2w-9}{2w+7}$$