( \frac { 3 } { x - 2 } - \frac { 5 } { x + 3 } = \frac { 1 } { x ^ { 2 } + x - 6 }
Solve for x
x=9
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\left(x+3\right)\times 3-\left(x-2\right)\times 5=1
Variable x cannot be equal to any of the values -3,2 since division by zero is not defined. Multiply both sides of the equation by \left(x-2\right)\left(x+3\right), the least common multiple of x-2,x+3,x^{2}+x-6.
3x+9-\left(x-2\right)\times 5=1
Use the distributive property to multiply x+3 by 3.
3x+9-\left(5x-10\right)=1
Use the distributive property to multiply x-2 by 5.
3x+9-5x+10=1
To find the opposite of 5x-10, find the opposite of each term.
-2x+9+10=1
Combine 3x and -5x to get -2x.
-2x+19=1
Add 9 and 10 to get 19.
-2x=1-19
Subtract 19 from both sides.
-2x=-18
Subtract 19 from 1 to get -18.
x=\frac{-18}{-2}
Divide both sides by -2.
x=9
Divide -18 by -2 to get 9.
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