Solve f(-1)(x+2)+2(-4)(-1)/(x-1)(x+1)=

$$\frac { f ( - 1 ) ( x + 2 ) + 2 ( - 4 ) ( - 1 ) } { ( x - 1 ) ( x + 1 ) } =$$

Evaluate

$$\frac{8-2f-fx}{x^{2}-1}$$

$$|x|\neq 1$$

Short Solution Steps

Multiply 2 and -4 to get -8.

$$\frac{f\left(-1\right)\left(x+2\right)-8\left(-1\right)}{\left(x-1\right)\left(x+1\right)}$$

Multiply -8 and -1 to get 8.

$$\frac{f\left(-1\right)\left(x+2\right)+8}{\left(x-1\right)\left(x+1\right)}$$

Use the distributive property to multiply f\left(-1\right) by x+2.

$$\frac{-fx+2f\left(-1\right)+8}{\left(x-1\right)\left(x+1\right)}$$

Multiply 2 and -1 to get -2.

$$\frac{-fx-2f+8}{\left(x-1\right)\left(x+1\right)}$$

Consider \left(x-1\right)\left(x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{-fx-2f+8}{x^{2}-1^{2}}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{-fx-2f+8}{x^{2}-1}$$

Expand

$$\frac{8-2f-fx}{x^{2}-1}$$

$$|x|\neq 1$$

Short Solution Steps

Multiply 2 and -4 to get -8.

$$\frac{f\left(-1\right)\left(x+2\right)-8\left(-1\right)}{\left(x-1\right)\left(x+1\right)}$$

Multiply -8 and -1 to get 8.

$$\frac{f\left(-1\right)\left(x+2\right)+8}{\left(x-1\right)\left(x+1\right)}$$

Use the distributive property to multiply f\left(-1\right) by x+2.

$$\frac{-fx+2f\left(-1\right)+8}{\left(x-1\right)\left(x+1\right)}$$

Multiply 2 and -1 to get -2.

$$\frac{-fx-2f+8}{\left(x-1\right)\left(x+1\right)}$$

Consider \left(x-1\right)\left(x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{-fx-2f+8}{x^{2}-1^{2}}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{-fx-2f+8}{x^{2}-1}$$