Solve 3/(x+6)(x+1)5x/(x+2)(x-2)

$$\frac { 3 } { ( x + 6 ) ( x + 1 ) } \frac { 5 x } { ( x + 2 ) ( x - 2 ) }$$

Evaluate

$$\frac{15x}{\left(x+1\right)\left(x+6\right)\left(x^{2}-4\right)}$$

Short Solution Steps

Apply the distributive property by multiplying each term of x+6 by each term of x+1.

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

Combine x and 6x to get 7x.

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

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

$$\frac{3}{x^{2}+7x+6}\times \frac{5x}{x^{2}-2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{3}{x^{2}+7x+6}\times \frac{5x}{x^{2}-4}$$

Multiply \frac{3}{x^{2}+7x+6} times \frac{5x}{x^{2}-4} by multiplying numerator times numerator and denominator times denominator.

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

Multiply 3 and 5 to get 15.

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

Apply the distributive property by multiplying each term of x^{2}+7x+6 by each term of x^{2}-4.

$$\frac{15x}{x^{4}-4x^{2}+7x^{3}-28x+6x^{2}-24}$$

Combine -4x^{2} and 6x^{2} to get 2x^{2}.

$$\frac{15x}{x^{4}+2x^{2}+7x^{3}-28x-24}$$

Expand

$$\frac{15x}{\left(x+1\right)\left(x+6\right)\left(x^{2}-4\right)}$$

Short Solution Steps

Apply the distributive property by multiplying each term of x+6 by each term of x+1.

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

Combine x and 6x to get 7x.

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

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

$$\frac{3}{x^{2}+7x+6}\times \frac{5x}{x^{2}-2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{3}{x^{2}+7x+6}\times \frac{5x}{x^{2}-4}$$

Multiply \frac{3}{x^{2}+7x+6} times \frac{5x}{x^{2}-4} by multiplying numerator times numerator and denominator times denominator.

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

Multiply 3 and 5 to get 15.

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

Apply the distributive property by multiplying each term of x^{2}+7x+6 by each term of x^{2}-4.

$$\frac{15x}{x^{4}-4x^{2}+7x^{3}-28x+6x^{2}-24}$$

Combine -4x^{2} and 6x^{2} to get 2x^{2}.

$$\frac{15x}{x^{4}+2x^{2}+7x^{3}-28x-24}$$