Solve for x
x=1
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Linear Equation
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\frac{ 7 }{ 2x-3 } + \frac{ 3 }{ x+2 } = \frac{ 6 }{ 2x-3 }
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\left(x+2\right)\times 7+\left(2x-3\right)\times 3=\left(x+2\right)\times 6
Variable x cannot be equal to any of the values -2,\frac{3}{2} since division by zero is not defined. Multiply both sides of the equation by \left(2x-3\right)\left(x+2\right), the least common multiple of 2x-3,x+2.
7x+14+\left(2x-3\right)\times 3=\left(x+2\right)\times 6
Use the distributive property to multiply x+2 by 7.
7x+14+6x-9=\left(x+2\right)\times 6
Use the distributive property to multiply 2x-3 by 3.
13x+14-9=\left(x+2\right)\times 6
Combine 7x and 6x to get 13x.
13x+5=\left(x+2\right)\times 6
Subtract 9 from 14 to get 5.
13x+5=6x+12
Use the distributive property to multiply x+2 by 6.
13x+5-6x=12
Subtract 6x from both sides.
7x+5=12
Combine 13x and -6x to get 7x.
7x=12-5
Subtract 5 from both sides.
7x=7
Subtract 5 from 12 to get 7.
x=\frac{7}{7}
Divide both sides by 7.
x=1
Divide 7 by 7 to get 1.
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