Solve 2(4t)/9s(4t)-3(9s)/4t(9s)

$$\frac { 2 ( 4 t ) } { 9 s ( 4 t ) } - \frac { 3 ( 9 s ) } { 4 t ( 9 s ) }$$

Evaluate

$$\frac{8t-27s}{36st}$$

Short Solution Steps

Cancel out 2\times 2t in both numerator and denominator.

$$\frac{2}{9s}-\frac{3\times 9s}{4t\times 9s}$$

Cancel out 3\times 3s in both numerator and denominator.

$$\frac{2}{9s}-\frac{3}{4t}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9s and 4t is 36st. Multiply \frac{2}{9s} times \frac{4t}{4t}. Multiply \frac{3}{4t} times \frac{9s}{9s}.

$$\frac{2\times 4t}{36st}-\frac{3\times 9s}{36st}$$

Since \frac{2\times 4t}{36st} and \frac{3\times 9s}{36st} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times 4t-3\times 9s}{36st}$$

Do the multiplications in 2\times 4t-3\times 9s.

$$\frac{8t-27s}{36st}$$

Factor

$$\frac{-\frac{27s}{t}+8}{36s}$$