Question

x+3/x-2- 1-x /x=17/ 4​

Answer 1

Step-by-step explanation:

Let's solve your equation step-by-step.

x+3x−2−1−xx=174

x+3x+−2+−1+−1=174

Multiply all terms by x and cancel:

xx+3+−2x+−1x+−1x=17x4

x2−4x+3=174x(Simplify both sides of the equation)

x2−4x+3−174x=174x−174x(Subtract 17/4x from both sides)

x2+−334x+3=0

For this equation: a=1, b=-8.25, c=3

1x2+−8.25x+3=0

x=−b±√b2−4ac2a(Use quadratic formula with a=1, b=-8.25, c=3)

x=−(−8.25)±√(−8.25)2−4(1)(3)2(1)

x=8.25±√56.06252

x=7.868744782967984,0.3812552170320158

Check answers. (Plug them in to make sure they work.)

x=7.868745(Works in original equation)

x=0.381255(Works in original equation)

Answer:

x=7.868745 or x=0.381255

Answer 2

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We have

(x + 3)/(x-2)-(1-x)/x = 17/4

⇒ x(x + 3) - (1-x) (x - 2)/x(x - 2) = 17/4

⇒ 2x² + 2/x² - 2x = 17/4

⇒ 8x² + 8 = 17x² - 34x

9x² - 34x - 8 = 0

By using factorization method, we get

⇒ 9x² - 36x + 2x - 8 = 0

9x² - 36x + 2x - 8 = 0

9x(x-4) + 2(x - 4) = 0

(x-4) (9x + 2) = 0

⇒ x 4 = 0 or 9x + 2 = 0

⇒ x = 4,- 2/9 (As x can't be negative)

⇒ x = 4

But here, x = 4,- 2/9