Question

Solve the following quadratic equation: 2/x+1 +3/2(x-2) = 23/5x

Answer 1

Given:

2/x+1 +3/2(x-2) = 23/5x
2x /x+1 +3x /2(x-2) = 23/5
2×2x(x-2) + 3x (x+1) / 2(x+1)(x-2) = 23/5
4x² -8x +3x²+3x / 2(x² - x -2) = 23/5
4x² +3x²+3x-8x / 2(x² - x -2) = 23/5
7x² - 5x / 2(x² - x -2) = 23/5
5(7x² - 5x) = 23( 2(x² - x -2))
35x² -25x = 46(x² - x -2)
35x² -25x = 46x² - 46 x -92
46x² - 35x² - 46 x + 25x -92 = 0
11x² -21x -92= 0

Here, a= 11, b= -21 ,c = -92

x = -b ±√b² -4ac /2a  [quadratic formula]

x =( -(-21) ± √ (-21)² - 4×11× -92 )/ (2× 11)
x = (21±√ 441 +4408 )/ 22
x =( 21 ± √ 4489) /22
x = (21 ± 67) /22
x = (21+67)/22 = 88/22= 4
x =4
x = (21 - 67) /22
x = - 46/22  = -23/11
x = -23/11

HOPE THIS WILL HELP YOU....

Answer 2

Hey!!!

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Your answer-

2x+1+32(x−2)=23/5x
⇒4(x−2)+3(x+1)2(x+1)(x−2)=23/5x
⇒4x−8+3x+32(x2−2x+x−2)=23/5x
⇒5x(7x−5)=46(x2−x−2)
⇒35x2−25x=46x2−46x−92
⇒11x2−21x−92=0
⇒x=21±(−21)2−4×11×(−92)√2×11
⇒x=21±4489√22
⇒x=21±67/22
⇒x=88/22 or x=−46/22
⇒x=4 or x=−23/11

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I Hope It's help you...!!!!!