Solve 4/x+5/x^2/frac{16{x^2}-25/x}

$$\frac { \frac { 4 } { x } + \frac { 5 } { x ^ { 2 } } } { \frac { 16 } { x ^ { 2 } } - \frac { 25 } { x } }$$

Evaluate

$$-\frac{4x+5}{25x-16}$$

Short Solution Steps

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

$$\frac{\frac{4x}{x^{2}}+\frac{5}{x^{2}}}{\frac{16}{x^{2}}-\frac{25}{x}}$$

Since \frac{4x}{x^{2}} and \frac{5}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4x+5}{x^{2}}}{\frac{16}{x^{2}}-\frac{25}{x}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{2} and x is x^{2}. Multiply \frac{25}{x} times \frac{x}{x}.

$$\frac{\frac{4x+5}{x^{2}}}{\frac{16}{x^{2}}-\frac{25x}{x^{2}}}$$

Since \frac{16}{x^{2}} and \frac{25x}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4x+5}{x^{2}}}{\frac{16-25x}{x^{2}}}$$

Divide \frac{4x+5}{x^{2}} by \frac{16-25x}{x^{2}} by multiplying \frac{4x+5}{x^{2}} by the reciprocal of \frac{16-25x}{x^{2}}.

$$\frac{\left(4x+5\right)x^{2}}{x^{2}\left(16-25x\right)}$$

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

$$\frac{4x+5}{-25x+16}$$

Expand

$$\frac{4x+5}{16-25x}$$

Short Solution Steps

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

$$\frac{\frac{4x}{x^{2}}+\frac{5}{x^{2}}}{\frac{16}{x^{2}}-\frac{25}{x}}$$

Since \frac{4x}{x^{2}} and \frac{5}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4x+5}{x^{2}}}{\frac{16}{x^{2}}-\frac{25}{x}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{2} and x is x^{2}. Multiply \frac{25}{x} times \frac{x}{x}.

$$\frac{\frac{4x+5}{x^{2}}}{\frac{16}{x^{2}}-\frac{25x}{x^{2}}}$$

Since \frac{16}{x^{2}} and \frac{25x}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4x+5}{x^{2}}}{\frac{16-25x}{x^{2}}}$$

Divide \frac{4x+5}{x^{2}} by \frac{16-25x}{x^{2}} by multiplying \frac{4x+5}{x^{2}} by the reciprocal of \frac{16-25x}{x^{2}}.

$$\frac{\left(4x+5\right)x^{2}}{x^{2}\left(16-25x\right)}$$

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

$$\frac{4x+5}{-25x+16}$$