Question

can you solve this fast please ​

Answer 1

Question :--- solve for x :- 2/(x+1) + 3/2(x-2) = 23/5x , where , x ≠ 0, -1 , 2 .

Solution :---

→ 2/(x+1) + 3/2(x-2) = 23/5x

Taking LCM of denominator in LHS , we wet,

→ [ 2*2*(x-2) + 3(x+1) ] /2(x+1)(x-2) = 23/5x

→ [ 4x - 8 + 3x + 3 ] / [ 2x² - 2x -4 ] = 23/5x

Cross - Multiply Now,

→ 35x² - 25x = 46x² - 46x - 92

→ 46x² - 35x² - 46x + 25x -92 = 0

→ 11x² - 21x - 92 = 0

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Now, According to Sridharacharya formula for solving Quadratic Equation ax² + bx + c = 0, have Roots :---

==>> [ -b ± √(b²-4ac) ] / 2a

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we have to Solve 11x² - 21x - 92 = 0

Here,

→ a = 11

→ b = (-21)

→ c = (-92)

Putting all Values in above Formula we get,

==>> [ 21 ± √(441 + 4048) ] / 2*11

==>> [ 21 ± √4489 ] / 22

==>> [ 21 ± 67 ] /22

So, we get,

→ x = (21+67)/22 , or, → x = (21-67)/22

→ x = 4 or, → x = (-23)/11

Hence, value of x will be 4 and (-23/11) .

Answer 2

❏QuesTion :-

$\bf \: Solve \: for \: x \: \\ \to \: \frac{2}{x + 1} + \frac{3}{2(x - 2)} = \frac{23}{5x} , x ≠ 0 , - 1 , 2 \:$

❏Answer :-

$\to \boxed{x = \frac{ - 23}{11} \: or \: 4} \: \:$

❏Solution :-

We have ,

$\to \: \frac{2}{x + 1} + \frac{3}{2(x - 2)} = \frac{23}{5x} \: \\ \\ \sf{Taking \: LCM \: } \\ \\ \to \: \frac{4(x - 2) + 3(x + 1)}{2(x + 1)(x - 2)} = \frac{23}{5x} \\ \\ \to \: \frac{4x - 8 + 3x + 3}{2(x + 1)(x - 2)} = \frac{23}{5x} \\ \\ \to \: \frac{7x - 5}{2(x + 1)(x - 2)} = \: \frac{23}{5x} \\ \\ \sf \: Cross \: multiplication \\ \to \: 5x(7x - 5) = 46( {x}^{2} - 2x + x - 2) \\ \\ \to \: 35 {x}^{2} - 25x = 46 {x}^{2} - 46x - 92 \\ \\ \to \: 46 {x}^{2} - 35 {x}^{2} - 46x + 25x - 92 = 0 \\ \\ \to \: 11 {x}^{2} - 21x - 92 = 0 \\ \sf</p><p>Now \: apply \: shri \: dharacharya \: formula \: \\ \\ \to \: x = \frac{ - ( - 21) + \sqrt{ {( - 21)}^{2} - 4 \times 11 \times ( - 92) } }{2 \times 11} \\ \: \: \: or \: \frac{ - ( - 21) - \sqrt{ {( - 21)}^{2} - 4 \times 11 \times ( - 92) } }{2 \times 11} \: \\ \\ \to \: x = \frac{21 - \sqrt{441 + 44 \times 92} }{22} \: or \: \frac{21 + \sqrt{441 + 44 \times 92} }{22} \: \\ \\ \to \: x = \frac{21 - 67}{22} \: or \: \frac{21 + 67}{22} \\ \\ \to \: x = \frac{ - 46}{22} \: or \: \frac{88}{22} \\ \\ \to \boxed{x = \frac{ - 23}{11} \: or \: 4} \:$