Solve 4x^2/left(x-7right)left(x-3right)5left(x-7right)/x+3/2

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

Evaluate

$$\frac{10x^{2}}{x^{2}-9}$$

Short Solution Steps

Multiply \frac{4x^{2}}{\left(x-7\right)\left(x-3\right)} times \frac{5\left(x-7\right)}{x+3} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out x-7 in both numerator and denominator.

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

Express \frac{\frac{4\times 5x^{2}}{\left(x-3\right)\left(x+3\right)}}{2} as a single fraction.

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

Cancel out 2 in both numerator and denominator.

$$\frac{2\times 5x^{2}}{\left(x-3\right)\left(x+3\right)}$$

Multiply 2 and 5 to get 10.

$$\frac{10x^{2}}{\left(x-3\right)\left(x+3\right)}$$

Consider \left(x-3\right)\left(x+3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 3.

$$\frac{10x^{2}}{x^{2}-9}$$

Expand

$$\frac{10x^{2}}{x^{2}-9}$$

Short Solution Steps

Multiply \frac{4x^{2}}{\left(x-7\right)\left(x-3\right)} times \frac{5\left(x-7\right)}{x+3} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out x-7 in both numerator and denominator.

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

Express \frac{\frac{4\times 5x^{2}}{\left(x-3\right)\left(x+3\right)}}{2} as a single fraction.

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

Cancel out 2 in both numerator and denominator.

$$\frac{2\times 5x^{2}}{\left(x-3\right)\left(x+3\right)}$$

Multiply 2 and 5 to get 10.

$$\frac{10x^{2}}{\left(x-3\right)\left(x+3\right)}$$

Consider \left(x-3\right)\left(x+3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 3.

$$\frac{10x^{2}}{x^{2}-9}$$