What is the answer to (3x)/((x-3)(x-4))=2x+9 ?

The answer to (3x)/((x-3)(x-4))=2x+9 is x= 9/2 ,x=-1+sqrt(13),x=-1-sqrt(13)

Solve for x: (3x)/((x-3)(x-4))=2x+9

The solution is x= 9/2 ,x=-1+sqrt(13),x=-1-sqrt(13)

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\frac{3 x}{( x - 3 ) ( x - 4 )} = 2 x + 9

x = \frac{9}{2}, x = - 1 + 13, x = - 1 - 13

Decimal Notation

x = 4.5, x = 2.60555 \dots, x = - 4.60555 \dots

Solution steps

\frac{3 x}{( x - 3 ) ( x - 4 )} = 2 x + 9

Multiply both sides by

(x - 3) (x - 4)

3 x = 2 x (x - 3) (x - 4) + 9 (x - 3) (x - 4)

Solve

3 x = 2 x (x - 3) (x - 4) + 9 (x - 3) (x - 4) : x = \frac{9}{2}, x = - 1 + 13, x = - 1 - 13

x = \frac{9}{2}, x = - 1 + 13, x = - 1 - 13

Verify Solutions

Find undefined (singularity) points:

x = 3, x = 4

Combine undefined points with solutions:

x = \frac{9}{2}, x = - 1 + 13, x = - 1 - 13

\frac{1}{( h + 6 )} (h + 6) = 1

\frac{10}{x} = 5

n, I = \frac{n E}{n r + r}

15 x^{- 2} - 2 x^{- 1} - 1 = 0

\frac{32}{x} = - 8

What is the answer to (3x)/((x-3)(x-4))=2x+9 ?
The answer to (3x)/((x-3)(x-4))=2x+9 is x= 9/2 ,x=-1+sqrt(13),x=-1-sqrt(13)
Solve for x: (3x)/((x-3)(x-4))=2x+9
The solution is x= 9/2 ,x=-1+sqrt(13),x=-1-sqrt(13)