Question

x+2 /2x²+10x²+12/
please answer the question
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Answer 1

Given

x+2 /2x²+10x²+12/

ANSWER

SOLUTION :  

Given : (x - 1)/(2x + 1) +  (2x + 1)/(x - 1) = 5/2

[ (x - 1) (x - 1) +  (2x + 1) (2x + 1)] / [(2x + 1) (x - 1)] = 5/2

[ By taking LCM]

[(x - 1)² + (2x +1)²] /[2x² −2x + x + 1] = 5/2

[(x² + 1² - 2x ) +  ((2x)² + 1² + 2×2x )] / [2x² − x - 1] = 5/2

[(a + b)² = a² + b² + 2ab & (a - b)² = a² + b² - 2ab]

[x² + 1 - 2x  + 4x² + 1 + 4x )] /[2x² − x - 1] = 5/2

[5x² + 2x  +2 ] / [2x² − x - 1] = 5/2

2[5x² + 2x  +2]   = 5  [2x² − x -  1 ]

10x² + 4x + 4 = 10x² - 5x - 5

10x² - 10x² + 4x + 5x + 4 + 5 = 0

9x + 9 = 0

9x = - 9  

x = -9/9  

x = -1  

Hence, the roots of the quadratic equation  (x - 1)/(2x + 1) +  (2x + 1)/(x - 1) = 5/2  is -1 .

HOPE THIS ANSWER WILL HELP YOU….