Solve 12x^2/y^2-31x/y+20

$$12 \frac { x ^ { 2 } } { y ^ { 2 } } - 31 \frac { x } { y } + 20$$

Evaluate

$$\frac{\left(4y-3x\right)\left(5y-4x\right)}{y^{2}}$$

Short Solution Steps

Express 12\times \frac{x^{2}}{y^{2}} as a single fraction.

$$\frac{12x^{2}}{y^{2}}-31\times \frac{x}{y}+20$$

Express 31\times \frac{x}{y} as a single fraction.

$$\frac{12x^{2}}{y^{2}}-\frac{31x}{y}+20$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y^{2} and y is y^{2}. Multiply \frac{31x}{y} times \frac{y}{y}.

$$\frac{12x^{2}}{y^{2}}-\frac{31xy}{y^{2}}+20$$

Since \frac{12x^{2}}{y^{2}} and \frac{31xy}{y^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12x^{2}-31xy}{y^{2}}+20$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 20 times \frac{y^{2}}{y^{2}}.

$$\frac{12x^{2}-31xy}{y^{2}}+\frac{20y^{2}}{y^{2}}$$

Since \frac{12x^{2}-31xy}{y^{2}} and \frac{20y^{2}}{y^{2}} have the same denominator, add them by adding their numerators.

$$\frac{12x^{2}-31xy+20y^{2}}{y^{2}}$$

Differentiate w.r.t. x

$$\frac{24x-31y}{y^{2}}$$