Solve fol 1-2 x-3-1-x-5-1 1-9- x-3-2- 5

Given, 1/2x 3 + 1/x 5 = 1 1/9 x 5 + 2x 3/(2x 3)(x 5) = 10/9 3x 8/2x^2 13x + 15 = 10/9 9(3x 8) = 10(2x^2 13x + 15) 27x 72 = 20x^2 130x + 150 20x^2 157x + ...

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Byju's Answer

Standard X

Mathematics

Fundamental Theorem of Arithmetic

Solve fol 1/2...

Question

Solve for x :
$\frac{1}{2 x - 3} + \frac{1}{x - 5} = 1 \frac{1}{9}, x \neq \frac{3}{2}, 5$

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Solution

Given, $\frac{1}{2 x - 3} + \frac{1}{x - 5} = 1 \frac{1}{9}$
$\frac{x - 5 + 2 x - 3}{(2 x - 3) (x - 5)} = \frac{10}{9}$
$\frac{3 x - 8}{2 x^{2} - 13 x + 15} = \frac{10}{9}$
$9 (3 x - 8) = 10 (2 x^{2} - 13 x + 15)$
$27 x - 72 = 20 x^{2} - 130 x + 150$
$20 x^{2} - 157 x + 222 = 0$
$20 x^{2} - 120 x - 37 x + 222 = 0$
$20 x (x - 6) - 37 (x - 6) = 0$
$(x - 6) (20 x - 37) = 0$
Either x - 6 = 0 or 20x - 37 = 0
$\Rightarrow x = 6, x = \frac{37}{20}$

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Solve for x : 12x−3+1x−5=119,x≠32,5

Given, 12x−3+1x−5=119 x−5+2x−3(2x−3)(x−5)=109 3x−82x2−13x+15=109 9(3x−8)=10(2x2−13x+15) 27x−72=20x2−130x+150 20x2−157x+222=0 20x2−120x−37x+222=0 20x(x−6)−37(x−6)=0 (x−6)(20x−37)=0 Either x - 6 = 0 or 20x - 37 = 0 ⇒x=6,x=3720

Solve for x :
$\frac{1}{2 x - 3} + \frac{1}{x - 5} = 1 \frac{1}{9}, x \neq \frac{3}{2}, 5$