The roots of the equation 3x-5 - 2xx-3 - 5 are where x-3-5

3x 5 + 2xx 3 = 5 ∵ x≠3,5 ∴ The given equation can be re written as 3(x 3) +2x (x 5) = 5(x 5) (x 3) ⇒ 3x 9 +2x^2 10x = 5(x^2 8x+15) ⇒ 3x^2 33x+ 84 = 0 ⇒ x^2 1 ...

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The roots of ...

Question

The roots of the equation $\frac{3}{x - 5} + \frac{2 x}{x - 3} = 5$ are (where $x \neq 3, 5$ )

5

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6

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7

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4

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Solution

The correct option is D $4$
$\frac{3}{x - 5} + \frac{2 x}{x - 3} = 5$
$∵ x \neq 3, 5$
$∴$ The given equation can be re-written as
$3 (x - 3) + 2 x (x - 5) = 5 (x - 5) (x - 3) \Rightarrow 3 x - 9 + 2 x^{2} - 10 x = 5 (x^{2} - 8 x + 15)$
$\Rightarrow 3 x^{2} - 33 x + 84 = 0 \Rightarrow x^{2} - 11 x + 28 = 0 \Rightarrow (x - 4) (x - 7) = 0 ∴ x = 4, 7$

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The roots of the equation 3x−5+2xx−3=5 are (where x≠3,5)

The correct option is D 43x−5+2xx−3=5 ∵x≠3,5 ∴ The given equation can be re-written as 3(x−3)+2x(x−5)=5(x−5)(x−3)⇒3x−9+2x2−10x=5(x2−8x+15) ⇒3x2−33x+84=0⇒x2−11x+28=0⇒(x−4)(x−7)=0∴x=4,7

The roots of the equation $\frac{3}{x - 5} + \frac{2 x}{x - 3} = 5$ are (where $x \neq 3, 5$ )