Solve 1/y+4/frac{1{y}-9}

$$\frac { \frac { 1 } { y } + 4 } { \frac { 1 } { y } - 9 }$$

Evaluate

$$\frac{4y+1}{1-9y}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{y}{y}.

$$\frac{\frac{1}{y}+\frac{4y}{y}}{\frac{1}{y}-9}$$

Since \frac{1}{y} and \frac{4y}{y} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1+4y}{y}}{\frac{1}{y}-9}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 9 times \frac{y}{y}.

$$\frac{\frac{1+4y}{y}}{\frac{1}{y}-\frac{9y}{y}}$$

Since \frac{1}{y} and \frac{9y}{y} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1+4y}{y}}{\frac{1-9y}{y}}$$

Divide \frac{1+4y}{y} by \frac{1-9y}{y} by multiplying \frac{1+4y}{y} by the reciprocal of \frac{1-9y}{y}.

$$\frac{\left(1+4y\right)y}{y\left(1-9y\right)}$$

Cancel out y in both numerator and denominator.

$$\frac{4y+1}{-9y+1}$$

Expand

$$\frac{4y+1}{1-9y}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{y}{y}.

$$\frac{\frac{1}{y}+\frac{4y}{y}}{\frac{1}{y}-9}$$

Since \frac{1}{y} and \frac{4y}{y} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1+4y}{y}}{\frac{1}{y}-9}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 9 times \frac{y}{y}.

$$\frac{\frac{1+4y}{y}}{\frac{1}{y}-\frac{9y}{y}}$$

Since \frac{1}{y} and \frac{9y}{y} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1+4y}{y}}{\frac{1-9y}{y}}$$

Divide \frac{1+4y}{y} by \frac{1-9y}{y} by multiplying \frac{1+4y}{y} by the reciprocal of \frac{1-9y}{y}.

$$\frac{\left(1+4y\right)y}{y\left(1-9y\right)}$$

Cancel out y in both numerator and denominator.

$$\frac{4y+1}{-9y+1}$$