What is the answer to x/((x^2-5x+6))+((x^2-9))/(((x-3)^2))=1 ?

The answer to x/((x^2-5x+6))+((x^2-9))/(((x-3)^2))=1 is x= 12/7

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x/((x^2-5x+6))+((x^2-9))/(((x-3)^2))=1

\frac{x}{( x ^{2} - 5 x + 6 )} + \frac{( x ^{2} - 9 )}{( ( x - 3 ) ^{2} )} = 1

x = \frac{12}{7}

Decimal Notation

x = 1.71428 \dots

Solution steps

\frac{x}{( x ^{2} - 5 x + 6 )} + \frac{( x ^{2} - 9 )}{( ( x - 3 ) ^{2} )} = 1

Multiply by LCM

x^{2} + 2 x - 6 = x^{2} - 5 x + 6

Move

6

to the right side

x^{2} + 2 x = x^{2} - 5 x + 12

Subtract

x^{2} - 5 x

from both sides

x^{2} + 2 x - (x^{2} - 5 x) = x^{2} - 5 x + 12 - (x^{2} - 5 x)

Simplify

7 x = 12

Divide both sides by

7

x = \frac{12}{7}

Verify Solutions

Find undefined (singularity) points:

x = 2, x = 3

Combine undefined points with solutions:

x = \frac{12}{7}

\frac{36}{x} = \frac{x}{4}

\frac{22 - 4}{5 x} = 2

\frac{39}{2 - 3 x ^{2}} = \frac{15}{2}

\frac{x + 9}{x + 6} = 0

\frac{( x ( x - 1 ) )}{( x ^{2} + x - 2 )} = \frac{x}{( x + 5 )}

What is the answer to x/((x^2-5x+6))+((x^2-9))/(((x-3)^2))=1 ?
The answer to x/((x^2-5x+6))+((x^2-9))/(((x-3)^2))=1 is x= 12/7
Solve for x: x/((x^2-5x+6))+((x^2-9))/(((x-3)^2))=1
The solution is x= 12/7