Solve x/x^2-6x+9-4/x-3=3/x-3

$$\frac { x } { x ^ { 2 } - 6 x + 9 } - \frac { 4 } { x - 3 } = \frac { 3 } { x - 3 }$$

Solve for x

$$x = \frac{7}{2} = 3\frac{1}{2} = 3.5$$

Steps for Solving Linear Equation

Variable x cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by \left(x-3\right)^{2}, the least common multiple of x^{2}-6x+9,x-3.

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

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

$$x-\left(4x-12\right)=\left(x-3\right)\times 3$$

To find the opposite of 4x-12, find the opposite of each term.

$$x-4x+12=\left(x-3\right)\times 3$$

Combine x and -4x to get -3x.

$$-3x+12=\left(x-3\right)\times 3$$

Use the distributive property to multiply x-3 by 3.

$$-3x+12=3x-9$$

Subtract 3x from both sides.

$$-3x+12-3x=-9$$

Combine -3x and -3x to get -6x.

$$-6x+12=-9$$

Subtract 12 from both sides.

$$-6x=-9-12$$

Subtract 12 from -9 to get -21.

$$-6x=-21$$

Divide both sides by -6.

$$x=\frac{-21}{-6}$$

Reduce the fraction \frac{-21}{-6} to lowest terms by extracting and canceling out -3.

$$x=\frac{7}{2}$$