Solve x-2/x^2+2x-3-x+1/x^2-9=4/x^2-4x+3

$$\frac { x - 2 } { x ^ { 2 } + 2 x - 3 } - \frac { x + 1 } { x ^ { 2 } - 9 } = \frac { 4 } { x ^ { 2 } - 4 x + 3 }$$

Solve for x

$$x=-\frac{5}{9}\approx -0.555555556$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -3,1,3 since division by zero is not defined. Multiply both sides of the equation by \left(x-3\right)\left(x-1\right)\left(x+3\right), the least common multiple of x^{2}+2x-3,x^{2}-9,x^{2}-4x+3.

$$\left(x-3\right)\left(x-2\right)-\left(x-1\right)\left(x+1\right)=\left(x+3\right)\times 4$$

Use the distributive property to multiply x-3 by x-2 and combine like terms.

$$x^{2}-5x+6-\left(x-1\right)\left(x+1\right)=\left(x+3\right)\times 4$$

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}. Square 1.

$$x^{2}-5x+6-\left(x^{2}-1\right)=\left(x+3\right)\times 4$$

To find the opposite of x^{2}-1, find the opposite of each term.

$$x^{2}-5x+6-x^{2}+1=\left(x+3\right)\times 4$$

Combine x^{2} and -x^{2} to get 0.

$$-5x+6+1=\left(x+3\right)\times 4$$

Add 6 and 1 to get 7.

$$-5x+7=\left(x+3\right)\times 4$$

Use the distributive property to multiply x+3 by 4.

$$-5x+7=4x+12$$

Subtract 4x from both sides.

$$-5x+7-4x=12$$

Combine -5x and -4x to get -9x.

$$-9x+7=12$$

Subtract 7 from both sides.

$$-9x=12-7$$

Subtract 7 from 12 to get 5.

$$-9x=5$$

Divide both sides by -9.

$$x=\frac{5}{-9}$$

Fraction \frac{5}{-9} can be rewritten as -\frac{5}{9} by extracting the negative sign.

$$x=-\frac{5}{9}$$