Solve 1/x+8/x^2/frac{y{x^2}}

$$\frac { \frac { 1 } { x } + \frac { 8 } { x ^ { 2 } } } { \frac { y } { x ^ { 2 } } }$$

Evaluate

$$\frac{x+8}{y}$$

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{1}{x} times \frac{x}{x}.

$$\frac{\frac{x}{x^{2}}+\frac{8}{x^{2}}}{\frac{y}{x^{2}}}$$

Since \frac{x}{x^{2}} and \frac{8}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x+8}{x^{2}}}{\frac{y}{x^{2}}}$$

Divide \frac{x+8}{x^{2}} by \frac{y}{x^{2}} by multiplying \frac{x+8}{x^{2}} by the reciprocal of \frac{y}{x^{2}}.

$$\frac{\left(x+8\right)x^{2}}{x^{2}y}$$

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

$$\frac{x+8}{y}$$

Expand

$$\frac{x+8}{y}$$

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{1}{x} times \frac{x}{x}.

$$\frac{\frac{x}{x^{2}}+\frac{8}{x^{2}}}{\frac{y}{x^{2}}}$$

Since \frac{x}{x^{2}} and \frac{8}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x+8}{x^{2}}}{\frac{y}{x^{2}}}$$

Divide \frac{x+8}{x^{2}} by \frac{y}{x^{2}} by multiplying \frac{x+8}{x^{2}} by the reciprocal of \frac{y}{x^{2}}.

$$\frac{\left(x+8\right)x^{2}}{x^{2}y}$$

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

$$\frac{x+8}{y}$$