Solve x(x-3)*-7/x^2-3x

$$x(x-3) \times \frac{ -7 }{ { x }^{ 2 } -3x }$$

Evaluate

$$-7$$

Short Solution Steps

Express x\times \frac{-7}{x^{2}-3x} as a single fraction.

$$\frac{x\left(-7\right)}{x^{2}-3x}\left(x-3\right)$$

Use the distributive property to multiply \frac{x\left(-7\right)}{x^{2}-3x} by x-3.

$$\frac{x\left(-7\right)}{x^{2}-3x}x-3\times \frac{x\left(-7\right)}{x^{2}-3x}$$

Factor the expressions that are not already factored in \frac{x\left(-7\right)}{x^{2}-3x}.

$$\frac{-7x}{x\left(x-3\right)}x-3\times \frac{x\left(-7\right)}{x^{2}-3x}$$

Cancel out x in both numerator and denominator.

$$\frac{-7}{x-3}x-3\times \frac{x\left(-7\right)}{x^{2}-3x}$$

Express \frac{-7}{x-3}x as a single fraction.

$$\frac{-7x}{x-3}-3\times \frac{x\left(-7\right)}{x^{2}-3x}$$

Factor the expressions that are not already factored in \frac{x\left(-7\right)}{x^{2}-3x}.

$$\frac{-7x}{x-3}-3\times \frac{-7x}{x\left(x-3\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{-7x}{x-3}-3\times \frac{-7}{x-3}$$

Express -3\times \frac{-7}{x-3} as a single fraction.

$$\frac{-7x}{x-3}+\frac{-3\left(-7\right)}{x-3}$$

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

$$\frac{-7x-3\left(-7\right)}{x-3}$$

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

$$\frac{-7x+21}{x-3}$$

Factor the expressions that are not already factored in \frac{-7x+21}{x-3}.

$$\frac{7\left(-x+3\right)}{x-3}$$

Extract the negative sign in 3-x.

$$\frac{-7\left(x-3\right)}{x-3}$$

Cancel out x-3 in both numerator and denominator.

$$-7$$

Factor

$$-7$$