Solve 1/y-3/2/frac{1{y}+3/4}

$$\frac{ \frac{ 1 }{ y } - \frac{ 3 }{ 2 } }{ \frac{ 1 }{ y } + \frac{ 3 }{ 4 } }$$

Evaluate

$$-\frac{2\left(3y-2\right)}{3y+4}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and 2 is 2y. Multiply \frac{1}{y} times \frac{2}{2}. Multiply \frac{3}{2} times \frac{y}{y}.

$$\frac{\frac{2}{2y}-\frac{3y}{2y}}{\frac{1}{y}+\frac{3}{4}}$$

Since \frac{2}{2y} and \frac{3y}{2y} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2-3y}{2y}}{\frac{1}{y}+\frac{3}{4}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and 4 is 4y. Multiply \frac{1}{y} times \frac{4}{4}. Multiply \frac{3}{4} times \frac{y}{y}.

$$\frac{\frac{2-3y}{2y}}{\frac{4}{4y}+\frac{3y}{4y}}$$

Since \frac{4}{4y} and \frac{3y}{4y} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2-3y}{2y}}{\frac{4+3y}{4y}}$$

Divide \frac{2-3y}{2y} by \frac{4+3y}{4y} by multiplying \frac{2-3y}{2y} by the reciprocal of \frac{4+3y}{4y}.

$$\frac{\left(2-3y\right)\times 4y}{2y\left(4+3y\right)}$$

Cancel out 2y in both numerator and denominator.

$$\frac{2\left(-3y+2\right)}{3y+4}$$

Use the distributive property to multiply 2 by -3y+2.

$$\frac{-6y+4}{3y+4}$$

Expand

$$-\frac{2\left(3y-2\right)}{3y+4}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and 2 is 2y. Multiply \frac{1}{y} times \frac{2}{2}. Multiply \frac{3}{2} times \frac{y}{y}.

$$\frac{\frac{2}{2y}-\frac{3y}{2y}}{\frac{1}{y}+\frac{3}{4}}$$

Since \frac{2}{2y} and \frac{3y}{2y} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2-3y}{2y}}{\frac{1}{y}+\frac{3}{4}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and 4 is 4y. Multiply \frac{1}{y} times \frac{4}{4}. Multiply \frac{3}{4} times \frac{y}{y}.

$$\frac{\frac{2-3y}{2y}}{\frac{4}{4y}+\frac{3y}{4y}}$$

Since \frac{4}{4y} and \frac{3y}{4y} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2-3y}{2y}}{\frac{4+3y}{4y}}$$

Divide \frac{2-3y}{2y} by \frac{4+3y}{4y} by multiplying \frac{2-3y}{2y} by the reciprocal of \frac{4+3y}{4y}.

$$\frac{\left(2-3y\right)\times 4y}{2y\left(4+3y\right)}$$

Cancel out 2y in both numerator and denominator.

$$\frac{2\left(-3y+2\right)}{3y+4}$$

Use the distributive property to multiply 2 by -3y+2.

$$\frac{-6y+4}{3y+4}$$