What is the answer to ((x^2-2x)(2x-2)-9(2x-2))/((x^2-2x))=0 ?

The answer to ((x^2-2x)(2x-2)-9(2x-2))/((x^2-2x))=0 is x=1,x=1+sqrt(10),x=1-sqrt(10)

Solve for x: ((x^2-2x)(2x-2)-9(2x-2))/((x^2-2x))=0

The solution is x=1,x=1+sqrt(10),x=1-sqrt(10)

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\frac{( x ^{2} - 2 x ) ( 2 x - 2 ) - 9 ( 2 x - 2 )}{( x ^{2} - 2 x )} = 0

x = 1, x = 1 + 10, x = 1 - 10

Decimal Notation

x = 1, x = 4.16227 \dots, x = - 2.16227 \dots

Solution steps

\frac{( x ^{2} - 2 x ) ( 2 x - 2 ) - 9 ( 2 x - 2 )}{( x ^{2} - 2 x )} = 0

Simplify

\frac{( x ^{2} - 2 x ) ( 2 x - 2 ) - 9 ( 2 x - 2 )}{x ^{2} - 2 x} : \frac{2 x ^{3} - 6 x ^{2} - 14 x + 18}{x ^{2} - 2 x}

\frac{2 x ^{3} - 6 x ^{2} - 14 x + 18}{x ^{2} - 2 x} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

2 x^{3} - 6 x^{2} - 14 x + 18 = 0

Solve

2 x^{3} - 6 x^{2} - 14 x + 18 = 0 : x = 1, x = 1 + 10, x = 1 - 10

x = 1, x = 1 + 10, x = 1 - 10

Verify Solutions

Find undefined (singularity) points:

x = 0, x = 2

Combine undefined points with solutions:

x = 1, x = 1 + 10, x = 1 - 10

x, \frac{4}{x} - \frac{5}{y} = 2

\frac{51}{2 - 3 x} = \frac{4}{3}

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

100 - x = \frac{98.2818 - 10}{11 x}

\frac{3}{2 x - 1 + 4} = \frac{6 x}{2 x - 1}

What is the answer to ((x^2-2x)(2x-2)-9(2x-2))/((x^2-2x))=0 ?
The answer to ((x^2-2x)(2x-2)-9(2x-2))/((x^2-2x))=0 is x=1,x=1+sqrt(10),x=1-sqrt(10)
Solve for x: ((x^2-2x)(2x-2)-9(2x-2))/((x^2-2x))=0
The solution is x=1,x=1+sqrt(10),x=1-sqrt(10)