Question

Solve it using quadratic formula.


grade 9
10 points​

Answer 1

1. {-1/4, 1}
2. {3/4, 6}

Explanation:

1. We can clear fractions and solve the resulting quadratic. We clear fractions by multiplying the equation by the product of the denominators.

`(2x+1)/(2x-1)-(2x-1)/(2x+1)=(8)/(3)\\\\3((2x+1)^2-(2x-1)^2)=8(2x-1)(2x+1)\\\\3(8x) = 8(4x^2 -1)\\\\4x^2 -3x -1 = 0\qquad\text{factor out 8, subtract 3x}\\\\x=(-(-3)\pm√((-3)^2-4(4)(-1)))/(2(4))=(3\pm√(25))/(8)\\\\x=(3\pm5)/(8)=\left\{-(1)/(4),1\right\}`

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2. Using the same idea here, we get ...

`(2)/(x-2)+(3)/(x)=(9)/(x+3)\\\\2(x)(x+3)+3(x-2)(x+3)=9(x-2)(x)\\\\2x^2+6x+3(x^2+x-6)=9x^2-18x\\\\4x^2-27x+18=0\\\\x=(-(-27)\pm√((-27)^2-4(4)(18)))/(2(4))=(27\pm√(441))/(8)\\\\x=(27\pm21)/(8)=\left\{(3)/(4),6\right\}`