Solve 2x-3/x+1*2x-5/x-1=

$$\frac { 2 x - 3 } { x + 1 } \times \frac { 2 x - 5 } { x - 1 } =$$

Evaluate

$$\frac{\left(2x-5\right)\left(2x-3\right)}{x^{2}-1}$$

Short Solution Steps

Multiply \frac{2x-3}{x+1} times \frac{2x-5}{x-1} by multiplying numerator times numerator and denominator times denominator.

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

Apply the distributive property by multiplying each term of 2x-3 by each term of 2x-5.

$$\frac{4x^{2}-10x-6x+15}{\left(x+1\right)\left(x-1\right)}$$

Combine -10x and -6x to get -16x.

$$\frac{4x^{2}-16x+15}{\left(x+1\right)\left(x-1\right)}$$

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}.

$$\frac{4x^{2}-16x+15}{x^{2}-1^{2}}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{4x^{2}-16x+15}{x^{2}-1}$$

Expand

$$\frac{4x^{2}-16x+15}{x^{2}-1}$$

Short Solution Steps

Multiply \frac{2x-3}{x+1} times \frac{2x-5}{x-1} by multiplying numerator times numerator and denominator times denominator.

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

Apply the distributive property by multiplying each term of 2x-3 by each term of 2x-5.

$$\frac{4x^{2}-10x-6x+15}{\left(x+1\right)\left(x-1\right)}$$

Combine -10x and -6x to get -16x.

$$\frac{4x^{2}-16x+15}{\left(x+1\right)\left(x-1\right)}$$

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}.

$$\frac{4x^{2}-16x+15}{x^{2}-1^{2}}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{4x^{2}-16x+15}{x^{2}-1}$$