Solve 3/4-2x/y-1+7x-y/1-y

$$\frac{ 3 }{ 4 } - \frac{ 2x }{ y-1 } + \frac{ 7x-y }{ 1-y }$$

Evaluate

$$\frac{36x-7y+3}{4\left(1-y\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and y-1 is 4\left(y-1\right). Multiply \frac{3}{4} times \frac{y-1}{y-1}. Multiply \frac{2x}{y-1} times \frac{4}{4}.

$$\frac{3\left(y-1\right)}{4\left(y-1\right)}-\frac{4\times 2x}{4\left(y-1\right)}+\frac{7x-y}{1-y}$$

Since \frac{3\left(y-1\right)}{4\left(y-1\right)} and \frac{4\times 2x}{4\left(y-1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(y-1\right)-4\times 2x}{4\left(y-1\right)}+\frac{7x-y}{1-y}$$

Do the multiplications in 3\left(y-1\right)-4\times 2x.

$$\frac{3y-3-8x}{4\left(y-1\right)}+\frac{7x-y}{1-y}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4\left(y-1\right) and 1-y is 4\left(y-1\right). Multiply \frac{7x-y}{1-y} times \frac{-4}{-4}.

$$\frac{3y-3-8x}{4\left(y-1\right)}+\frac{-4\left(7x-y\right)}{4\left(y-1\right)}$$

Since \frac{3y-3-8x}{4\left(y-1\right)} and \frac{-4\left(7x-y\right)}{4\left(y-1\right)} have the same denominator, add them by adding their numerators.

$$\frac{3y-3-8x-4\left(7x-y\right)}{4\left(y-1\right)}$$

Do the multiplications in 3y-3-8x-4\left(7x-y\right).

$$\frac{3y-3-8x-28x+4y}{4\left(y-1\right)}$$

Combine like terms in 3y-3-8x-28x+4y.

$$\frac{7y-3-36x}{4\left(y-1\right)}$$

Expand 4\left(y-1\right).

$$\frac{7y-3-36x}{4y-4}$$

Expand

$$\frac{-36x+7y-3}{4\left(y-1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and y-1 is 4\left(y-1\right). Multiply \frac{3}{4} times \frac{y-1}{y-1}. Multiply \frac{2x}{y-1} times \frac{4}{4}.

$$\frac{3\left(y-1\right)}{4\left(y-1\right)}-\frac{4\times 2x}{4\left(y-1\right)}+\frac{7x-y}{1-y}$$

Since \frac{3\left(y-1\right)}{4\left(y-1\right)} and \frac{4\times 2x}{4\left(y-1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(y-1\right)-4\times 2x}{4\left(y-1\right)}+\frac{7x-y}{1-y}$$

Do the multiplications in 3\left(y-1\right)-4\times 2x.

$$\frac{3y-3-8x}{4\left(y-1\right)}+\frac{7x-y}{1-y}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4\left(y-1\right) and 1-y is 4\left(y-1\right). Multiply \frac{7x-y}{1-y} times \frac{-4}{-4}.

$$\frac{3y-3-8x}{4\left(y-1\right)}+\frac{-4\left(7x-y\right)}{4\left(y-1\right)}$$

Since \frac{3y-3-8x}{4\left(y-1\right)} and \frac{-4\left(7x-y\right)}{4\left(y-1\right)} have the same denominator, add them by adding their numerators.

$$\frac{3y-3-8x-4\left(7x-y\right)}{4\left(y-1\right)}$$

Do the multiplications in 3y-3-8x-4\left(7x-y\right).

$$\frac{3y-3-8x-28x+4y}{4\left(y-1\right)}$$

Combine like terms in 3y-3-8x-28x+4y.

$$\frac{7y-3-36x}{4\left(y-1\right)}$$

Expand 4\left(y-1\right).

$$\frac{7y-3-36x}{4y-4}$$