Solve 6+2a/8a-3-4a+8/9a+4=

$$\frac { 6 + 2 a } { 8 a - 3 } - \frac { 4 a + 8 } { 9 a + 4 } =$$

Evaluate

$$-\frac{2\left(7a^{2}-5a-24\right)}{\left(8a-3\right)\left(9a+4\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8a-3 and 9a+4 is \left(8a-3\right)\left(9a+4\right). Multiply \frac{6+2a}{8a-3} times \frac{9a+4}{9a+4}. Multiply \frac{4a+8}{9a+4} times \frac{8a-3}{8a-3}.

$$\frac{\left(6+2a\right)\left(9a+4\right)}{\left(8a-3\right)\left(9a+4\right)}-\frac{\left(4a+8\right)\left(8a-3\right)}{\left(8a-3\right)\left(9a+4\right)}$$

Since \frac{\left(6+2a\right)\left(9a+4\right)}{\left(8a-3\right)\left(9a+4\right)} and \frac{\left(4a+8\right)\left(8a-3\right)}{\left(8a-3\right)\left(9a+4\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(6+2a\right)\left(9a+4\right)-\left(4a+8\right)\left(8a-3\right)}{\left(8a-3\right)\left(9a+4\right)}$$

Do the multiplications in \left(6+2a\right)\left(9a+4\right)-\left(4a+8\right)\left(8a-3\right).

$$\frac{54a+24+18a^{2}+8a-32a^{2}+12a-64a+24}{\left(8a-3\right)\left(9a+4\right)}$$

Combine like terms in 54a+24+18a^{2}+8a-32a^{2}+12a-64a+24.

$$\frac{10a+48-14a^{2}}{\left(8a-3\right)\left(9a+4\right)}$$

Expand \left(8a-3\right)\left(9a+4\right).

$$\frac{10a+48-14a^{2}}{72a^{2}+5a-12}$$

Expand

$$-\frac{2\left(7a^{2}-5a-24\right)}{\left(8a-3\right)\left(9a+4\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8a-3 and 9a+4 is \left(8a-3\right)\left(9a+4\right). Multiply \frac{6+2a}{8a-3} times \frac{9a+4}{9a+4}. Multiply \frac{4a+8}{9a+4} times \frac{8a-3}{8a-3}.

$$\frac{\left(6+2a\right)\left(9a+4\right)}{\left(8a-3\right)\left(9a+4\right)}-\frac{\left(4a+8\right)\left(8a-3\right)}{\left(8a-3\right)\left(9a+4\right)}$$

Since \frac{\left(6+2a\right)\left(9a+4\right)}{\left(8a-3\right)\left(9a+4\right)} and \frac{\left(4a+8\right)\left(8a-3\right)}{\left(8a-3\right)\left(9a+4\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(6+2a\right)\left(9a+4\right)-\left(4a+8\right)\left(8a-3\right)}{\left(8a-3\right)\left(9a+4\right)}$$

Do the multiplications in \left(6+2a\right)\left(9a+4\right)-\left(4a+8\right)\left(8a-3\right).

$$\frac{54a+24+18a^{2}+8a-32a^{2}+12a-64a+24}{\left(8a-3\right)\left(9a+4\right)}$$

Combine like terms in 54a+24+18a^{2}+8a-32a^{2}+12a-64a+24.

$$\frac{10a+48-14a^{2}}{\left(8a-3\right)\left(9a+4\right)}$$

Expand \left(8a-3\right)\left(9a+4\right).

$$\frac{10a+48-14a^{2}}{72a^{2}+5a-12}$$