Solve- 22 x-1 x-3-3 x-32 x-1-5- x -3-12

2(2x #160; #8722; #160;1x #160;+ #160;3) #160; #8722; #160;3(x #160;+ #160;32x #160; #8722; #160;1) #160;= #160;5 #8658; #160; ...

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Byju's Answer

Standard X

Mathematics

Solving a Quadratic Equation by Factorization Method

Solve: 22 x-1...

Question

Solve: $2 (\frac{2 x - 1}{x + 3}) - 3 (\frac{x + 3}{2 x - 1}) = 5, x \neq - 3, \frac{1}{2} .$

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Solution

$2 (\frac{2 x - 1}{x + 3}) - 3 (\frac{x + 3}{2 x - 1}) = 5 ⇒ \frac{4 x - 2}{x + 3} - \frac{3 x + 9}{2 x - 1} = 5 ⇒ \frac{(4 x - 2) (2 x - 1) - (x + 3) (3 x + 9)}{(x + 3) (2 x - 1)} = 5 ⇒ 8 x^{2} - 4 x - 4 x + 2 - (3 x^{2} + 9 x + 9 x + 27) = 5 (2 x^{2} - x + 6 x - 3) ⇒ 8 x^{2} - 8 x + 2 - 3 x^{2} - 9 x - 9 x - 27 = 10 x^{2} - 5 x + 30 x - 15 ⇒ 10 x^{2} - 5 x^{2} + 25 x + 26 x - 15 + 25 = 0 ⇒ 5 x^{2} + 51 x + 10 = 0 \Rightarrow 5 x^{2} + 50 x + x + 10 = 0 \Rightarrow 5 x (x + 10) + 1 (x + 10) = 0 \Rightarrow (x + 10) (5 x + 1) = 0 ∴ x = - 10, x = - \frac{1}{5}$

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Similar questions

2 (\frac{2 x - 1}{x + 3}) - 3 (\frac{x + 3}{2 x - 1}) = 5, (x \neq - 3, \frac{1}{2})

Q. Solve of

x

2 (\frac{2 x - 1}{x + 3}) - 3 (\frac{x + 3}{2 x - 1}) = 5

Solve for x:
$(i) \frac{x - 1}{x - 2} + \frac{x - 3}{x - 4} = 3 \frac{1}{3}; x \neq 2, 4 (i i) \frac{1}{x} + \frac{2}{2 x - 3} = \frac{1}{x - 2}, x \neq 0, \frac{3}{2}, 2 (i i i) x + \frac{1}{x} = 3, x \neq 0 (i v) \frac{16}{x} - 1 = \frac{15}{x + 1}, x \neq 0, - 1 (v) \frac{1}{x - 3} - \frac{1}{x + 5} = \frac{1}{6}, x \neq 3, - 5,$

Q. Solve:

2 (\frac{2 x - 1}{x + 3}) - 3 (\frac{x + 3}{2 x - 1}) = ?

Solve the following equations for x:

(i) $2^{2 x} - 2^{x + 3} + 2^{4}$ =0

(ii) $3^{2 x + 4} + 1 = 2 . 3^{x + 2}$

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Solve: 22x-1x+3-3x+32x-1=5, x≠-3,12.

Solve: $2 (\frac{2 x - 1}{x + 3}) - 3 (\frac{x + 3}{2 x - 1}) = 5, x \neq - 3, \frac{1}{2} .$