Solve a(b-3a)^2/3a^2-ab-3a

$$\frac { a ( b - 3 a ) ^ { 2 } } { 3 a ^ { 2 } - a b } - 3 a$$

Evaluate

$$-b$$

Short Solution Steps

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

$$\frac{a\left(-3a+b\right)^{2}}{a\left(3a-b\right)}-3a$$

Cancel out a in both numerator and denominator.

$$\frac{\left(-3a+b\right)^{2}}{3a-b}-3a$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -3a times \frac{3a-b}{3a-b}.

$$\frac{\left(-3a+b\right)^{2}}{3a-b}+\frac{-3a\left(3a-b\right)}{3a-b}$$

Since \frac{\left(-3a+b\right)^{2}}{3a-b} and \frac{-3a\left(3a-b\right)}{3a-b} have the same denominator, add them by adding their numerators.

$$\frac{\left(-3a+b\right)^{2}-3a\left(3a-b\right)}{3a-b}$$

Do the multiplications in \left(-3a+b\right)^{2}-3a\left(3a-b\right).

$$\frac{9a^{2}-6ab+b^{2}-9a^{2}+3ab}{3a-b}$$

Combine like terms in 9a^{2}-6ab+b^{2}-9a^{2}+3ab.

$$\frac{b^{2}-3ab}{3a-b}$$

Factor the expressions that are not already factored in \frac{b^{2}-3ab}{3a-b}.

$$\frac{b\left(-3a+b\right)}{3a-b}$$

Extract the negative sign in b-3a.

$$\frac{-b\left(3a-b\right)}{3a-b}$$

Cancel out 3a-b in both numerator and denominator.

$$-b$$

Expand

$$-b$$

Short Solution Steps

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

$$\frac{a\left(-3a+b\right)^{2}}{a\left(3a-b\right)}-3a$$

Cancel out a in both numerator and denominator.

$$\frac{\left(-3a+b\right)^{2}}{3a-b}-3a$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -3a times \frac{3a-b}{3a-b}.

$$\frac{\left(-3a+b\right)^{2}}{3a-b}+\frac{-3a\left(3a-b\right)}{3a-b}$$

Since \frac{\left(-3a+b\right)^{2}}{3a-b} and \frac{-3a\left(3a-b\right)}{3a-b} have the same denominator, add them by adding their numerators.

$$\frac{\left(-3a+b\right)^{2}-3a\left(3a-b\right)}{3a-b}$$

Do the multiplications in \left(-3a+b\right)^{2}-3a\left(3a-b\right).

$$\frac{9a^{2}-6ab+b^{2}-9a^{2}+3ab}{3a-b}$$

Combine like terms in 9a^{2}-6ab+b^{2}-9a^{2}+3ab.

$$\frac{b^{2}-3ab}{3a-b}$$

Factor the expressions that are not already factored in \frac{b^{2}-3ab}{3a-b}.

$$\frac{b\left(-3a+b\right)}{3a-b}$$

Extract the negative sign in b-3a.

$$\frac{-b\left(3a-b\right)}{3a-b}$$

Cancel out 3a-b in both numerator and denominator.

$$-b$$