Solve for x
x=\frac{8}{11}\approx 0.727272727
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Linear Equation
5 problems similar to:
\frac { ( 2 x + 3 ) ( x - 4 ) } { ( 2 x - 4 ) ( x + 5 ) } = 1
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\left(2x+3\right)\left(x-4\right)=2\left(x-2\right)\left(x+5\right)
Variable x cannot be equal to any of the values -5,2 since division by zero is not defined. Multiply both sides of the equation by 2\left(x-2\right)\left(x+5\right).
2x^{2}-5x-12=2\left(x-2\right)\left(x+5\right)
Use the distributive property to multiply 2x+3 by x-4 and combine like terms.
2x^{2}-5x-12=\left(2x-4\right)\left(x+5\right)
Use the distributive property to multiply 2 by x-2.
2x^{2}-5x-12=2x^{2}+6x-20
Use the distributive property to multiply 2x-4 by x+5 and combine like terms.
2x^{2}-5x-12-2x^{2}=6x-20
Subtract 2x^{2} from both sides.
-5x-12=6x-20
Combine 2x^{2} and -2x^{2} to get 0.
-5x-12-6x=-20
Subtract 6x from both sides.
-11x-12=-20
Combine -5x and -6x to get -11x.
-11x=-20+12
Add 12 to both sides.
-11x=-8
Add -20 and 12 to get -8.
x=\frac{-8}{-11}
Divide both sides by -11.
x=\frac{8}{11}
Fraction \frac{-8}{-11} can be simplified to \frac{8}{11} by removing the negative sign from both the numerator and the denominator.
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
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Limits
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