Solve a(4a-b)/3a-3b-a/3-b^2/a-b

$$\frac { a ( 4 a - b ) } { 3 a - 3 b } - \frac { a } { 3 } - \frac { b ^ { 2 } } { a - b }$$

Evaluate

$$a+b$$

Short Solution Steps

Factor 3a-3b.

$$\frac{a\left(4a-b\right)}{3\left(a-b\right)}-\frac{a}{3}-\frac{b^{2}}{a-b}$$

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

$$\frac{a\left(4a-b\right)}{3\left(a-b\right)}-\frac{a\left(a-b\right)}{3\left(a-b\right)}-\frac{b^{2}}{a-b}$$

Since \frac{a\left(4a-b\right)}{3\left(a-b\right)} and \frac{a\left(a-b\right)}{3\left(a-b\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{a\left(4a-b\right)-a\left(a-b\right)}{3\left(a-b\right)}-\frac{b^{2}}{a-b}$$

Do the multiplications in a\left(4a-b\right)-a\left(a-b\right).

$$\frac{4a^{2}-ab-a^{2}+ab}{3\left(a-b\right)}-\frac{b^{2}}{a-b}$$

Combine like terms in 4a^{2}-ab-a^{2}+ab.

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

Cancel out 3 in both numerator and denominator.

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

Since \frac{a^{2}}{a-b} and \frac{b^{2}}{a-b} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Cancel out a-b in both numerator and denominator.

$$a+b$$

Expand

$$a+b$$

Short Solution Steps

Factor 3a-3b.

$$\frac{a\left(4a-b\right)}{3\left(a-b\right)}-\frac{a}{3}-\frac{b^{2}}{a-b}$$

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

$$\frac{a\left(4a-b\right)}{3\left(a-b\right)}-\frac{a\left(a-b\right)}{3\left(a-b\right)}-\frac{b^{2}}{a-b}$$

Since \frac{a\left(4a-b\right)}{3\left(a-b\right)} and \frac{a\left(a-b\right)}{3\left(a-b\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{a\left(4a-b\right)-a\left(a-b\right)}{3\left(a-b\right)}-\frac{b^{2}}{a-b}$$

Do the multiplications in a\left(4a-b\right)-a\left(a-b\right).

$$\frac{4a^{2}-ab-a^{2}+ab}{3\left(a-b\right)}-\frac{b^{2}}{a-b}$$

Combine like terms in 4a^{2}-ab-a^{2}+ab.

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

Cancel out 3 in both numerator and denominator.

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

Since \frac{a^{2}}{a-b} and \frac{b^{2}}{a-b} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Cancel out a-b in both numerator and denominator.

$$a+b$$