Solve 1+2/4r-2-3t/6t

$$\frac { 1 + 2 } { 4 r } - \frac { 2 - 3 t } { 6 t }$$

Evaluate

$$\frac{6rt-4r+9t}{12rt}$$

Short Solution Steps

Add 1 and 2 to get 3.

$$\frac{3}{4r}-\frac{2-3t}{6t}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4r and 6t is 12rt. Multiply \frac{3}{4r} times \frac{3t}{3t}. Multiply \frac{2-3t}{6t} times \frac{2r}{2r}.

$$\frac{3\times 3t}{12rt}-\frac{\left(2-3t\right)\times 2r}{12rt}$$

Since \frac{3\times 3t}{12rt} and \frac{\left(2-3t\right)\times 2r}{12rt} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\times 3t-\left(2-3t\right)\times 2r}{12rt}$$

Do the multiplications in 3\times 3t-\left(2-3t\right)\times 2r.

$$\frac{9t-4r+6tr}{12rt}$$

Expand

$$\frac{6rt-4r+9t}{12rt}$$

Short Solution Steps

Add 1 and 2 to get 3.

$$\frac{3}{4r}-\frac{2-3t}{6t}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4r and 6t is 12rt. Multiply \frac{3}{4r} times \frac{3t}{3t}. Multiply \frac{2-3t}{6t} times \frac{2r}{2r}.

$$\frac{3\times 3t}{12rt}-\frac{\left(2-3t\right)\times 2r}{12rt}$$

Since \frac{3\times 3t}{12rt} and \frac{\left(2-3t\right)\times 2r}{12rt} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\times 3t-\left(2-3t\right)\times 2r}{12rt}$$

Do the multiplications in 3\times 3t-\left(2-3t\right)\times 2r.

$$\frac{9t-4r+6tr}{12rt}$$