Solve 43p/2x-7*8x^2-98/5y+3div12pq^2/15y+9

$$4 \frac { 3 p } { 2 x - 7 } \times \frac { 8 x ^ { 2 } - 98 } { 5 y + 3 } \div \frac { 12 p q ^ { 2 } } { 15 y + 9 }$$

Evaluate

$$\frac{6\left(2x+7\right)}{q^{2}}$$

Short Solution Steps

Express 4\times \frac{3p}{2x-7} as a single fraction.

$$\frac{\frac{4\times 3p}{2x-7}\times \frac{8x^{2}-98}{5y+3}}{\frac{12pq^{2}}{15y+9}}$$

Multiply \frac{4\times 3p}{2x-7} times \frac{8x^{2}-98}{5y+3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{4\times 3p\left(8x^{2}-98\right)}{\left(2x-7\right)\left(5y+3\right)}}{\frac{12pq^{2}}{15y+9}}$$

Factor the expressions that are not already factored in \frac{12pq^{2}}{15y+9}.

$$\frac{\frac{4\times 3p\left(8x^{2}-98\right)}{\left(2x-7\right)\left(5y+3\right)}}{\frac{12pq^{2}}{3\left(5y+3\right)}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\frac{4\times 3p\left(8x^{2}-98\right)}{\left(2x-7\right)\left(5y+3\right)}}{\frac{4pq^{2}}{5y+3}}$$

Divide \frac{4\times 3p\left(8x^{2}-98\right)}{\left(2x-7\right)\left(5y+3\right)} by \frac{4pq^{2}}{5y+3} by multiplying \frac{4\times 3p\left(8x^{2}-98\right)}{\left(2x-7\right)\left(5y+3\right)} by the reciprocal of \frac{4pq^{2}}{5y+3}.

$$\frac{4\times 3p\left(8x^{2}-98\right)\left(5y+3\right)}{\left(2x-7\right)\left(5y+3\right)\times 4pq^{2}}$$

Cancel out 4p\left(5y+3\right) in both numerator and denominator.

$$\frac{3\left(8x^{2}-98\right)}{\left(2x-7\right)q^{2}}$$

Factor the expressions that are not already factored.

$$\frac{2\times 3\left(2x-7\right)\left(2x+7\right)}{\left(2x-7\right)q^{2}}$$

Cancel out 2x-7 in both numerator and denominator.

$$\frac{2\times 3\left(2x+7\right)}{q^{2}}$$

Expand the expression.

$$\frac{12x+42}{q^{2}}$$

Expand

$$\frac{6\left(2x+7\right)}{q^{2}}$$

Short Solution Steps

Express 4\times \frac{3p}{2x-7} as a single fraction.

$$\frac{\frac{4\times 3p}{2x-7}\times \frac{8x^{2}-98}{5y+3}}{\frac{12pq^{2}}{15y+9}}$$

Multiply \frac{4\times 3p}{2x-7} times \frac{8x^{2}-98}{5y+3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{4\times 3p\left(8x^{2}-98\right)}{\left(2x-7\right)\left(5y+3\right)}}{\frac{12pq^{2}}{15y+9}}$$

Factor the expressions that are not already factored in \frac{12pq^{2}}{15y+9}.

$$\frac{\frac{4\times 3p\left(8x^{2}-98\right)}{\left(2x-7\right)\left(5y+3\right)}}{\frac{12pq^{2}}{3\left(5y+3\right)}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\frac{4\times 3p\left(8x^{2}-98\right)}{\left(2x-7\right)\left(5y+3\right)}}{\frac{4pq^{2}}{5y+3}}$$

Divide \frac{4\times 3p\left(8x^{2}-98\right)}{\left(2x-7\right)\left(5y+3\right)} by \frac{4pq^{2}}{5y+3} by multiplying \frac{4\times 3p\left(8x^{2}-98\right)}{\left(2x-7\right)\left(5y+3\right)} by the reciprocal of \frac{4pq^{2}}{5y+3}.

$$\frac{4\times 3p\left(8x^{2}-98\right)\left(5y+3\right)}{\left(2x-7\right)\left(5y+3\right)\times 4pq^{2}}$$

Cancel out 4p\left(5y+3\right) in both numerator and denominator.

$$\frac{3\left(8x^{2}-98\right)}{\left(2x-7\right)q^{2}}$$

Factor the expressions that are not already factored.

$$\frac{2\times 3\left(2x-7\right)\left(2x+7\right)}{\left(2x-7\right)q^{2}}$$

Cancel out 2x-7 in both numerator and denominator.

$$\frac{2\times 3\left(2x+7\right)}{q^{2}}$$

Expand the expression.

$$\frac{12x+42}{q^{2}}$$