Solve 3a-1/4a+4+1/a+1*67

$$\frac { 3 a - 1 } { 4 a + 4 } + \frac { 1 } { a + 1 } \cdot 67$$

Evaluate

$$\frac{3\left(a+89\right)}{4\left(a+1\right)}$$

Short Solution Steps

Express \frac{1}{a+1}\times 67 as a single fraction.

$$\frac{3a-1}{4a+4}+\frac{67}{a+1}$$

Factor 4a+4.

$$\frac{3a-1}{4\left(a+1\right)}+\frac{67}{a+1}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4\left(a+1\right) and a+1 is 4\left(a+1\right). Multiply \frac{67}{a+1} times \frac{4}{4}.

$$\frac{3a-1}{4\left(a+1\right)}+\frac{67\times 4}{4\left(a+1\right)}$$

Since \frac{3a-1}{4\left(a+1\right)} and \frac{67\times 4}{4\left(a+1\right)} have the same denominator, add them by adding their numerators.

$$\frac{3a-1+67\times 4}{4\left(a+1\right)}$$

Do the multiplications in 3a-1+67\times 4.

$$\frac{3a-1+268}{4\left(a+1\right)}$$

Combine like terms in 3a-1+268.

$$\frac{3a+267}{4\left(a+1\right)}$$

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

$$\frac{3a+267}{4a+4}$$

Expand

$$\frac{3\left(a+89\right)}{4\left(a+1\right)}$$

Short Solution Steps

Express \frac{1}{a+1}\times 67 as a single fraction.

$$\frac{3a-1}{4a+4}+\frac{67}{a+1}$$

Factor 4a+4.

$$\frac{3a-1}{4\left(a+1\right)}+\frac{67}{a+1}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4\left(a+1\right) and a+1 is 4\left(a+1\right). Multiply \frac{67}{a+1} times \frac{4}{4}.

$$\frac{3a-1}{4\left(a+1\right)}+\frac{67\times 4}{4\left(a+1\right)}$$

Since \frac{3a-1}{4\left(a+1\right)} and \frac{67\times 4}{4\left(a+1\right)} have the same denominator, add them by adding their numerators.

$$\frac{3a-1+67\times 4}{4\left(a+1\right)}$$

Do the multiplications in 3a-1+67\times 4.

$$\frac{3a-1+268}{4\left(a+1\right)}$$

Combine like terms in 3a-1+268.

$$\frac{3a+267}{4\left(a+1\right)}$$

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

$$\frac{3a+267}{4a+4}$$