Solve -a-1/4a+1-2/3

$$\frac { - a - 1 } { 4 a + 1 } - \frac { 2 } { 3 }$$

Evaluate

$$-\frac{11a+5}{3\left(4a+1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4a+1 and 3 is 3\left(4a+1\right). Multiply \frac{-a-1}{4a+1} times \frac{3}{3}. Multiply \frac{2}{3} times \frac{4a+1}{4a+1}.

$$\frac{3\left(-a-1\right)}{3\left(4a+1\right)}-\frac{2\left(4a+1\right)}{3\left(4a+1\right)}$$

Since \frac{3\left(-a-1\right)}{3\left(4a+1\right)} and \frac{2\left(4a+1\right)}{3\left(4a+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(-a-1\right)-2\left(4a+1\right)}{3\left(4a+1\right)}$$

Do the multiplications in 3\left(-a-1\right)-2\left(4a+1\right).

$$\frac{-3a-3-8a-2}{3\left(4a+1\right)}$$

Combine like terms in -3a-3-8a-2.

$$\frac{-11a-5}{3\left(4a+1\right)}$$

Expand 3\left(4a+1\right).

$$\frac{-11a-5}{12a+3}$$

Expand

$$-\frac{11a+5}{3\left(4a+1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4a+1 and 3 is 3\left(4a+1\right). Multiply \frac{-a-1}{4a+1} times \frac{3}{3}. Multiply \frac{2}{3} times \frac{4a+1}{4a+1}.

$$\frac{3\left(-a-1\right)}{3\left(4a+1\right)}-\frac{2\left(4a+1\right)}{3\left(4a+1\right)}$$

Since \frac{3\left(-a-1\right)}{3\left(4a+1\right)} and \frac{2\left(4a+1\right)}{3\left(4a+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(-a-1\right)-2\left(4a+1\right)}{3\left(4a+1\right)}$$

Do the multiplications in 3\left(-a-1\right)-2\left(4a+1\right).

$$\frac{-3a-3-8a-2}{3\left(4a+1\right)}$$

Combine like terms in -3a-3-8a-2.

$$\frac{-11a-5}{3\left(4a+1\right)}$$

Expand 3\left(4a+1\right).

$$\frac{-11a-5}{12a+3}$$