Solve 16/3x-6+9/4x-8

$$\frac { 16 } { 3 x - 6 } + \frac { 9 } { 4 x - 8 }$$

Evaluate

$$\frac{91}{12\left(x-2\right)}$$

Short Solution Steps

Factor 3x-6. Factor 4x-8.

$$\frac{16}{3\left(x-2\right)}+\frac{9}{4\left(x-2\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3\left(x-2\right) and 4\left(x-2\right) is 12\left(x-2\right). Multiply \frac{16}{3\left(x-2\right)} times \frac{4}{4}. Multiply \frac{9}{4\left(x-2\right)} times \frac{3}{3}.

$$\frac{16\times 4}{12\left(x-2\right)}+\frac{9\times 3}{12\left(x-2\right)}$$

Since \frac{16\times 4}{12\left(x-2\right)} and \frac{9\times 3}{12\left(x-2\right)} have the same denominator, add them by adding their numerators.

$$\frac{16\times 4+9\times 3}{12\left(x-2\right)}$$

Do the multiplications in 16\times 4+9\times 3.

$$\frac{64+27}{12\left(x-2\right)}$$

Do the calculations in 64+27.

$$\frac{91}{12\left(x-2\right)}$$

Expand 12\left(x-2\right).

$$\frac{91}{12x-24}$$

Factor

$$\frac{91}{12\left(x-2\right)}$$