Solve 3(5x-4)(x-7)/6x(6x+7)div4(x-7)/4x(x+3)

$$\frac { 3 ( 5 x - 4 ) ( x - 7 ) } { 6 x ( 6 x + 7 ) } \div \frac { 4 ( x - 7 ) } { 4 x ( x + 3 ) }$$

Evaluate

$$\frac{\left(5x-4\right)\left(x+3\right)}{2\left(6x+7\right)}$$

Short Solution Steps

Divide \frac{3\left(5x-4\right)\left(x-7\right)}{6x\left(6x+7\right)} by \frac{4\left(x-7\right)}{4x\left(x+3\right)} by multiplying \frac{3\left(5x-4\right)\left(x-7\right)}{6x\left(6x+7\right)} by the reciprocal of \frac{4\left(x-7\right)}{4x\left(x+3\right)}.

$$\frac{3\left(5x-4\right)\left(x-7\right)\times 4x\left(x+3\right)}{6x\left(6x+7\right)\times 4\left(x-7\right)}$$

Cancel out 2\times 2\times 3x\left(x-7\right) in both numerator and denominator.

$$\frac{\left(5x-4\right)\left(x+3\right)}{2\left(6x+7\right)}$$

Apply the distributive property by multiplying each term of 5x-4 by each term of x+3.

$$\frac{5x^{2}+15x-4x-12}{2\left(6x+7\right)}$$

Combine 15x and -4x to get 11x.

$$\frac{5x^{2}+11x-12}{2\left(6x+7\right)}$$

Use the distributive property to multiply 2 by 6x+7.

$$\frac{5x^{2}+11x-12}{12x+14}$$

Expand

$$\frac{5x^{2}+11x-12}{2\left(6x+7\right)}$$

Short Solution Steps

Divide \frac{3\left(5x-4\right)\left(x-7\right)}{6x\left(6x+7\right)} by \frac{4\left(x-7\right)}{4x\left(x+3\right)} by multiplying \frac{3\left(5x-4\right)\left(x-7\right)}{6x\left(6x+7\right)} by the reciprocal of \frac{4\left(x-7\right)}{4x\left(x+3\right)}.

$$\frac{3\left(5x-4\right)\left(x-7\right)\times 4x\left(x+3\right)}{6x\left(6x+7\right)\times 4\left(x-7\right)}$$

Cancel out 2\times 2\times 3x\left(x-7\right) in both numerator and denominator.

$$\frac{\left(5x-4\right)\left(x+3\right)}{2\left(6x+7\right)}$$

Apply the distributive property by multiplying each term of 5x-4 by each term of x+3.

$$\frac{5x^{2}+15x-4x-12}{2\left(6x+7\right)}$$

Combine 15x and -4x to get 11x.

$$\frac{5x^{2}+11x-12}{2\left(6x+7\right)}$$

Use the distributive property to multiply 2 by 6x+7.

$$\frac{5x^{2}+11x-12}{12x+14}$$