\frac { 5 x - 3 } { ( 2 x + 1 ) ( x + 2 } - \frac { 1 } { x + 2 } = \frac { 4 } { 2 x + 1 }
Solve for x
x=-12
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5x-3-\left(2x+1\right)=\left(x+2\right)\times 4
Variable x cannot be equal to any of the values -2,-\frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by \left(x+2\right)\left(2x+1\right), the least common multiple of \left(2x+1\right)\left(x+2\right),x+2,2x+1.
5x-3-2x-1=\left(x+2\right)\times 4
To find the opposite of 2x+1, find the opposite of each term.
3x-3-1=\left(x+2\right)\times 4
Combine 5x and -2x to get 3x.
3x-4=\left(x+2\right)\times 4
Subtract 1 from -3 to get -4.
3x-4=4x+8
Use the distributive property to multiply x+2 by 4.
3x-4-4x=8
Subtract 4x from both sides.
-x-4=8
Combine 3x and -4x to get -x.
-x=8+4
Add 4 to both sides.
-x=12
Add 8 and 4 to get 12.
x=-12
Multiply both sides by -1.
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