Solve [3a^2/2div4a/3]div6a/3x^2=

$$[ \frac { 3 a ^ { 2 } } { 2 } \div \frac { 4 a } { 3 } ] \div \frac { 6 a } { 3 x ^ { 2 } } =$$

Evaluate

$$\frac{9x^{2}}{16}$$

Solution Steps

Divide \frac{\frac{3a^{2}}{2}}{\frac{4a}{3}} by \frac{6a}{3x^{2}} by multiplying \frac{\frac{3a^{2}}{2}}{\frac{4a}{3}} by the reciprocal of \frac{6a}{3x^{2}}.

$$\frac{\frac{3a^{2}}{2}\times 3x^{2}}{\frac{4a}{3}\times 6a}$$

Express \frac{3a^{2}}{2}\times 3 as a single fraction.

$$\frac{\frac{3a^{2}\times 3}{2}x^{2}}{\frac{4a}{3}\times 6a}$$

Express \frac{3a^{2}\times 3}{2}x^{2} as a single fraction.

$$\frac{\frac{3a^{2}\times 3x^{2}}{2}}{\frac{4a}{3}\times 6a}$$

Cancel out 3, the greatest common factor in 6 and 3.

$$\frac{\frac{3a^{2}\times 3x^{2}}{2}}{2\times 4aa}$$

Multiply 3 and 3 to get 9.

$$\frac{\frac{9a^{2}x^{2}}{2}}{2\times 4aa}$$

Multiply a and a to get a^{2}.

$$\frac{\frac{9a^{2}x^{2}}{2}}{2\times 4a^{2}}$$

Multiply 2 and 4 to get 8.

$$\frac{\frac{9a^{2}x^{2}}{2}}{8a^{2}}$$

Express \frac{\frac{9a^{2}x^{2}}{2}}{8a^{2}} as a single fraction.

$$\frac{9a^{2}x^{2}}{2\times 8a^{2}}$$

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

$$\frac{9x^{2}}{2\times 8}$$

Multiply 2 and 8 to get 16.

$$\frac{9x^{2}}{16}$$

Differentiate w.r.t. x

$$\frac{9x}{8}$$