Solve frac{6x^{3}y^{5}}{35a^{2}b^{4}}div12x^4y^4/7a^4b^4

$$\frac { 6 x ^ { 3 } y ^ { 5 } } { 35 a ^ { 2 } b ^ { 4 } } \div \frac { 12 x ^ { 4 } y ^ { 4 } } { 7 a ^ { 4 } b ^ { 4 } }$$

Evaluate

$$\frac{ya^{2}}{10x}$$

Solution Steps

Divide \frac{6x^{3}y^{5}}{35a^{2}b^{4}} by \frac{12x^{4}y^{4}}{7a^{4}b^{4}} by multiplying \frac{6x^{3}y^{5}}{35a^{2}b^{4}} by the reciprocal of \frac{12x^{4}y^{4}}{7a^{4}b^{4}}.

$$\frac{6x^{3}y^{5}\times 7a^{4}b^{4}}{35a^{2}b^{4}\times 12x^{4}y^{4}}$$

Cancel out 6\times 7a^{2}x^{3}b^{4}y^{4} in both numerator and denominator.

$$\frac{ya^{2}}{2\times 5x}$$

Multiply 2 and 5 to get 10.

$$\frac{ya^{2}}{10x}$$

Differentiate w.r.t. x

$$-\frac{\left(\frac{a}{x}\right)^{2}y}{10}$$