Solve 3(x+3)/4-4(2x+3)/3

$$\frac { 3 ( x + 3 ) } { 4 } - \frac { 4 ( 2 x + 3 ) } { 3 }$$

Evaluate

$$-\frac{23x}{12}-\frac{7}{4}$$

Short Solution Steps

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

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

Since \frac{3\times 3\left(x+3\right)}{12} and \frac{4\times 4\left(2x+3\right)}{12} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 3\times 3\left(x+3\right)-4\times 4\left(2x+3\right).

$$\frac{9x+27-32x-48}{12}$$

Combine like terms in 9x+27-32x-48.

$$\frac{-23x-21}{12}$$

Expand

$$-\frac{23x}{12}-\frac{7}{4}$$

Short Solution Steps

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

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

Since \frac{3\times 3\left(x+3\right)}{12} and \frac{4\times 4\left(2x+3\right)}{12} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 3\times 3\left(x+3\right)-4\times 4\left(2x+3\right).

$$\frac{9x+27-32x-48}{12}$$

Combine like terms in 9x+27-32x-48.

$$\frac{-23x-21}{12}$$