Solve x+1/2x5x-300y/y-x

$$x + \frac { 1 } { 2 } x \frac { 5 x - 300 y } { y - x }$$

Evaluate

$$\frac{x\left(3x-298y\right)}{2\left(y-x\right)}$$

Short Solution Steps

Multiply \frac{1}{2} times \frac{5x-300y}{y-x} by multiplying numerator times numerator and denominator times denominator.

$$x+\frac{5x-300y}{2\left(y-x\right)}x$$

Use the distributive property to multiply 2 by y-x.

$$x+\frac{5x-300y}{2y-2x}x$$

Express \frac{5x-300y}{2y-2x}x as a single fraction.

$$x+\frac{\left(5x-300y\right)x}{2y-2x}$$

Factor 2y-2x.

$$x+\frac{\left(5x-300y\right)x}{2\left(-x+y\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{2\left(-x+y\right)}{2\left(-x+y\right)}.

$$\frac{x\times 2\left(-x+y\right)}{2\left(-x+y\right)}+\frac{\left(5x-300y\right)x}{2\left(-x+y\right)}$$

Since \frac{x\times 2\left(-x+y\right)}{2\left(-x+y\right)} and \frac{\left(5x-300y\right)x}{2\left(-x+y\right)} have the same denominator, add them by adding their numerators.

$$\frac{x\times 2\left(-x+y\right)+\left(5x-300y\right)x}{2\left(-x+y\right)}$$

Do the multiplications in x\times 2\left(-x+y\right)+\left(5x-300y\right)x.

$$\frac{-2x^{2}+2xy+5x^{2}-300yx}{2\left(-x+y\right)}$$

Combine like terms in -2x^{2}+2xy+5x^{2}-300yx.

$$\frac{3x^{2}-298xy}{2\left(-x+y\right)}$$

Expand 2\left(-x+y\right).

$$\frac{3x^{2}-298xy}{-2x+2y}$$

Expand

$$-\frac{298xy-3x^{2}}{2\left(y-x\right)}$$

Short Solution Steps

Multiply \frac{1}{2} times \frac{5x-300y}{y-x} by multiplying numerator times numerator and denominator times denominator.

$$x+\frac{5x-300y}{2\left(y-x\right)}x$$

Use the distributive property to multiply 2 by y-x.

$$x+\frac{5x-300y}{2y-2x}x$$

Express \frac{5x-300y}{2y-2x}x as a single fraction.

$$x+\frac{\left(5x-300y\right)x}{2y-2x}$$

Factor 2y-2x.

$$x+\frac{\left(5x-300y\right)x}{2\left(-x+y\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{2\left(-x+y\right)}{2\left(-x+y\right)}.

$$\frac{x\times 2\left(-x+y\right)}{2\left(-x+y\right)}+\frac{\left(5x-300y\right)x}{2\left(-x+y\right)}$$

Since \frac{x\times 2\left(-x+y\right)}{2\left(-x+y\right)} and \frac{\left(5x-300y\right)x}{2\left(-x+y\right)} have the same denominator, add them by adding their numerators.

$$\frac{x\times 2\left(-x+y\right)+\left(5x-300y\right)x}{2\left(-x+y\right)}$$

Do the multiplications in x\times 2\left(-x+y\right)+\left(5x-300y\right)x.

$$\frac{-2x^{2}+2xy+5x^{2}-300yx}{2\left(-x+y\right)}$$

Combine like terms in -2x^{2}+2xy+5x^{2}-300yx.

$$\frac{3x^{2}-298xy}{2\left(-x+y\right)}$$

Expand 2\left(-x+y\right).

$$\frac{3x^{2}-298xy}{-2x+2y}$$