Solve 7/xdiv4xy/x^2*12x^3/x^5

$$\frac { 7 } { x } \div \frac { 4 x y } { x ^ { 2 } } \cdot \frac { 12 x ^ { 3 } } { x ^ { 5 } }$$

Evaluate

$$\frac{21}{yx^{2}}$$

Solution Steps

Divide \frac{7}{x} by \frac{4xy}{x^{2}} by multiplying \frac{7}{x} by the reciprocal of \frac{4xy}{x^{2}}.

$$\frac{7x^{2}}{x\times 4xy}\times \frac{12x^{3}}{x^{5}}$$

Cancel out xx in both numerator and denominator.

$$\frac{7}{4y}\times \frac{12x^{3}}{x^{5}}$$

Cancel out x^{3} in both numerator and denominator.

$$\frac{7}{4y}\times \frac{12}{x^{2}}$$

Multiply \frac{7}{4y} times \frac{12}{x^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 12}{4yx^{2}}$$

Cancel out 4 in both numerator and denominator.

$$\frac{3\times 7}{yx^{2}}$$

Multiply 3 and 7 to get 21.

$$\frac{21}{yx^{2}}$$

Differentiate w.r.t. x

$$-\frac{42}{yx^{3}}$$