Solve -b/a-2a-b/3b-3b-a/6a

$$\frac { - b } { a } - \frac { 2 a - b } { 3 b } - \frac { 3 b - a } { 6 a }$$

Evaluate

$$\frac{-4a^{2}+3ab-9b^{2}}{6ab}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a and 3b is 3ab. Multiply \frac{-b}{a} times \frac{3b}{3b}. Multiply \frac{2a-b}{3b} times \frac{a}{a}.

$$\frac{\left(-b\right)\times 3b}{3ab}-\frac{\left(2a-b\right)a}{3ab}-\frac{3b-a}{6a}$$

Since \frac{\left(-b\right)\times 3b}{3ab} and \frac{\left(2a-b\right)a}{3ab} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(-b\right)\times 3b-\left(2a-b\right)a}{3ab}-\frac{3b-a}{6a}$$

Do the multiplications in \left(-b\right)\times 3b-\left(2a-b\right)a.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3ab and 6a is 6ab. Multiply \frac{-3b^{2}-2a^{2}+ba}{3ab} times \frac{2}{2}. Multiply \frac{3b-a}{6a} times \frac{b}{b}.

$$\frac{2\left(-3b^{2}-2a^{2}+ba\right)}{6ab}-\frac{\left(3b-a\right)b}{6ab}$$

Since \frac{2\left(-3b^{2}-2a^{2}+ba\right)}{6ab} and \frac{\left(3b-a\right)b}{6ab} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(-3b^{2}-2a^{2}+ba\right)-\left(3b-a\right)b}{6ab}$$

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

$$\frac{-6b^{2}-4a^{2}+2ba-3b^{2}+ba}{6ab}$$

Combine like terms in -6b^{2}-4a^{2}+2ba-3b^{2}+ba.

$$\frac{-9b^{2}+3ba-4a^{2}}{6ab}$$

Expand

$$-\frac{4a^{2}-3ab+9b^{2}}{6ab}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a and 3b is 3ab. Multiply \frac{-b}{a} times \frac{3b}{3b}. Multiply \frac{2a-b}{3b} times \frac{a}{a}.

$$\frac{\left(-b\right)\times 3b}{3ab}-\frac{\left(2a-b\right)a}{3ab}-\frac{3b-a}{6a}$$

Since \frac{\left(-b\right)\times 3b}{3ab} and \frac{\left(2a-b\right)a}{3ab} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(-b\right)\times 3b-\left(2a-b\right)a}{3ab}-\frac{3b-a}{6a}$$

Do the multiplications in \left(-b\right)\times 3b-\left(2a-b\right)a.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3ab and 6a is 6ab. Multiply \frac{-3b^{2}-2a^{2}+ba}{3ab} times \frac{2}{2}. Multiply \frac{3b-a}{6a} times \frac{b}{b}.

$$\frac{2\left(-3b^{2}-2a^{2}+ba\right)}{6ab}-\frac{\left(3b-a\right)b}{6ab}$$

Since \frac{2\left(-3b^{2}-2a^{2}+ba\right)}{6ab} and \frac{\left(3b-a\right)b}{6ab} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(-3b^{2}-2a^{2}+ba\right)-\left(3b-a\right)b}{6ab}$$

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

$$\frac{-6b^{2}-4a^{2}+2ba-3b^{2}+ba}{6ab}$$

Combine like terms in -6b^{2}-4a^{2}+2ba-3b^{2}+ba.

$$\frac{-9b^{2}+3ba-4a^{2}}{6ab}$$