What is the answer to (3x^2-5x)/(3x-2)-1= 2/(2-3x) ?

The answer to (3x^2-5x)/(3x-2)-1= 2/(2-3x) is x=2

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(3x^2-5x)/(3x-2)-1= 2/(2-3x)

\frac{3 x ^{2} - 5 x}{3 x - 2} - 1 = \frac{2}{2 - 3 x}

x = 2

Solution steps

\frac{3 x ^{2} - 5 x}{3 x - 2} - 1 = \frac{2}{2 - 3 x}

Multiply by LCM

(3 x^{2} - 5 x) (- 3 x + 2) - (3 x - 2) (- 3 x + 2) = 2 (3 x - 2)

Solve

(3 x^{2} - 5 x) (- 3 x + 2) - (3 x - 2) (- 3 x + 2) = 2 (3 x - 2) : x = 2, x = \frac{2}{3}

x = 2, x = \frac{2}{3}

Verify Solutions

Find undefined (singularity) points:

x = \frac{2}{3}

Since the equation is undefined for:

\frac{2}{3}

x = 2

G (x) = \frac{x ^{2} + 3 x - 5}{x + 6}

\frac{7}{2 x} - \frac{5}{3 x} = \frac{22}{3}

1 + \frac{4}{x - 6} = - \frac{x}{x - 6}

\frac{1}{2} + \frac{2}{x} = \frac{3}{4}

\frac{7}{x} - \frac{5}{4} = \frac{x}{8}

What is the answer to (3x^2-5x)/(3x-2)-1= 2/(2-3x) ?
The answer to (3x^2-5x)/(3x-2)-1= 2/(2-3x) is x=2
Solve for x: (3x^2-5x)/(3x-2)-1= 2/(2-3x)
The solution is x=2