Solve 12a^2-22a+8/3a-3a^2+2a-8/2a^2+4a

$$\frac { 12 a ^ { 2 } - 22 a + 8 } { 3 a } - \frac { 3 a ^ { 2 } + 2 a - 8 } { 2 a ^ { 2 } + 4 a }$$

Evaluate

$$4a-\frac{53}{6}+\frac{14}{3a}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{3a^{2}+2a-8}{2a^{2}+4a}.

$$\frac{12a^{2}-22a+8}{3a}-\frac{\left(3a-4\right)\left(a+2\right)}{2a\left(a+2\right)}$$

Cancel out a+2 in both numerator and denominator.

$$\frac{12a^{2}-22a+8}{3a}-\frac{3a-4}{2a}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3a and 2a is 6a. Multiply \frac{12a^{2}-22a+8}{3a} times \frac{2}{2}. Multiply \frac{3a-4}{2a} times \frac{3}{3}.

$$\frac{2\left(12a^{2}-22a+8\right)}{6a}-\frac{3\left(3a-4\right)}{6a}$$

Since \frac{2\left(12a^{2}-22a+8\right)}{6a} and \frac{3\left(3a-4\right)}{6a} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(12a^{2}-22a+8\right)-3\left(3a-4\right)}{6a}$$

Do the multiplications in 2\left(12a^{2}-22a+8\right)-3\left(3a-4\right).

$$\frac{24a^{2}-44a+16-9a+12}{6a}$$

Combine like terms in 24a^{2}-44a+16-9a+12.

$$\frac{24a^{2}-53a+28}{6a}$$

Expand

$$4a-\frac{53}{6}+\frac{14}{3a}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{3a^{2}+2a-8}{2a^{2}+4a}.

$$\frac{12a^{2}-22a+8}{3a}-\frac{\left(3a-4\right)\left(a+2\right)}{2a\left(a+2\right)}$$

Cancel out a+2 in both numerator and denominator.

$$\frac{12a^{2}-22a+8}{3a}-\frac{3a-4}{2a}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3a and 2a is 6a. Multiply \frac{12a^{2}-22a+8}{3a} times \frac{2}{2}. Multiply \frac{3a-4}{2a} times \frac{3}{3}.

$$\frac{2\left(12a^{2}-22a+8\right)}{6a}-\frac{3\left(3a-4\right)}{6a}$$

Since \frac{2\left(12a^{2}-22a+8\right)}{6a} and \frac{3\left(3a-4\right)}{6a} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(12a^{2}-22a+8\right)-3\left(3a-4\right)}{6a}$$

Do the multiplications in 2\left(12a^{2}-22a+8\right)-3\left(3a-4\right).

$$\frac{24a^{2}-44a+16-9a+12}{6a}$$

Combine like terms in 24a^{2}-44a+16-9a+12.

$$\frac{24a^{2}-53a+28}{6a}$$