Solve 3x/2-5y/frac{15y{2x}}

$$\frac{ 3x }{ 2 } - \frac{ 5y }{ \frac{ 15y }{ 2x } }$$

Evaluate

$$\frac{5x}{6}$$

Short Solution Steps

Divide 5y by \frac{15y}{2x} by multiplying 5y by the reciprocal of \frac{15y}{2x}.

$$\frac{3x}{2}-\frac{5y\times 2x}{15y}$$

Cancel out 5y in both numerator and denominator.

$$\frac{3x}{2}-\frac{2x}{3}$$

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

$$\frac{3\times 3x}{6}-\frac{2\times 2x}{6}$$

Since \frac{3\times 3x}{6} and \frac{2\times 2x}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\times 3x-2\times 2x}{6}$$

Do the multiplications in 3\times 3x-2\times 2x.

$$\frac{9x-4x}{6}$$

Combine like terms in 9x-4x.

$$\frac{5x}{6}$$

Differentiate w.r.t. x

$$\frac{5}{6} = 0.8333333333333334$$