Solve 3T-1/2+3/2T-2

$$\frac { 3 T - 1 } { 2 } + \frac { 3 } { 2 T - 2 }$$

Evaluate

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

Short Solution Steps

Factor 2T-2.

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

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

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

Since \frac{\left(3T-1\right)\left(T-1\right)}{2\left(T-1\right)} and \frac{3}{2\left(T-1\right)} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(3T-1\right)\left(T-1\right)+3.

$$\frac{3T^{2}-3T-T+1+3}{2\left(T-1\right)}$$

Combine like terms in 3T^{2}-3T-T+1+3.

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

Expand 2\left(T-1\right).

$$\frac{3T^{2}-4T+4}{2T-2}$$

Expand

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

Short Solution Steps

Factor 2T-2.

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

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

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

Since \frac{\left(3T-1\right)\left(T-1\right)}{2\left(T-1\right)} and \frac{3}{2\left(T-1\right)} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(3T-1\right)\left(T-1\right)+3.

$$\frac{3T^{2}-3T-T+1+3}{2\left(T-1\right)}$$

Combine like terms in 3T^{2}-3T-T+1+3.

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

Expand 2\left(T-1\right).

$$\frac{3T^{2}-4T+4}{2T-2}$$