Solve frac{20x^{4}y^{2}z^{3}}{7xy^5}*14y^2/40x^2z^3

$$\frac { 20 x ^ { 4 } y ^ { 2 } z ^ { 3 } } { 7 x y ^ { 5 } } \cdot \frac { 14 y ^ { 2 } } { 40 x ^ { 2 } z ^ { 3 } }$$

Evaluate

$$\frac{x}{y}$$

Solution Steps

Cancel out xy^{2} in both numerator and denominator.

$$\frac{20x^{3}z^{3}}{7y^{3}}\times \frac{14y^{2}}{40x^{2}z^{3}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{20x^{3}z^{3}}{7y^{3}}\times \frac{7y^{2}}{20x^{2}z^{3}}$$

Multiply \frac{20x^{3}z^{3}}{7y^{3}} times \frac{7y^{2}}{20x^{2}z^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{20x^{3}z^{3}\times 7y^{2}}{7y^{3}\times 20x^{2}z^{3}}$$

Cancel out 7\times 20x^{2}y^{2}z^{3} in both numerator and denominator.

$$\frac{x}{y}$$

Differentiate w.r.t. x

$$\frac{1}{y}$$