Question

Solve the rational equation.3/x + 3/x-2 = 3x -3/x-2

Answer 1

we have

3/x + 3/(x-2) = (3x -3)/(x-2)

step 1

​Multiply by x(x-2) both sides

3(x-2)+3x=(3x-3)x

apply distributive property both sides

3x-6+3x=3x^2-3x

6x-6=3x^2-3x

3x^2-3x-6x+6=0

3x^2-9x+6=0

Solve the quadratc equation

Solve by graphing

using a graphing tool

see the attached figure

please wait a minute

the solutions are x=1 and x=2

but remember that

the denominator can not be equal to zero

so

the value of x in the original expression can not be equal to 2

therefore

the solution is x=1

we have

3x^2-9x+6=0

Solve the quadratic equation using the formula

$x=\frac{-b_{\pm\sqrt[]{b^2-4ac}}}{2a}$

we have

a=3

b=-9

c=6

substitute

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