Question

Please answer this!!!

Answer 1

Solution :

$\longrightarrow \: \sf \dfrac{x - 4}{x - 5} + \dfrac{x - 6}{x - 7} = \dfrac{10}{3}$

$\sf \: \longrightarrow \dfrac{(x - 4)(x - 7) + (x - 6)(x - 5)}{(x - 5)(x - 7)} = \dfrac{10}{3}$

$\sf \longrightarrow \dfrac{ {x}^{2} - 7x - 4x + 28 + {x}^{2} - 5x - 6x + 30 }{ {x}^{2} - 7x - 5x + 35} = \dfrac{10}{ 3}$

$\sf \longrightarrow \dfrac{2 {x}^{2} - 22x + 58}{ {x}^{2} - 12x + 35 } = \dfrac{10}{3}$

$\sf \longrightarrow \dfrac{ {x}^{2} - 11x + 29 }{ {x}^{2} - 12x + 35} = \dfrac{5}{3}$

$\sf \longrightarrow 3( {x}^{2} - 11x + 29) = 5( {x}^{2} - 12x + 35)$

$\sf \longrightarrow 3 {x}^{2} - 33x + 87 = 5 {x}^{2} - 60x + 175$

$\sf \longrightarrow 2 {x}^{2} - 27x + 88 = 0$

$\sf \longrightarrow 2 {x}^{2} -16x - 11x + 88 = 0$

$\sf \longrightarrow 2x(x - 8) - 11(x - 8) = 0$

$\sf \longrightarrow (2x - 11)(x - 8) = 0$

$\sf \longrightarrow 2x - 11 = 0 \: or \: x - 8 = 0$

$\sf \longrightarrow x = \purple{ \dfrac{11}{2}} \: or \: x = \purple{ 8}$

Answer 2

Step-by-step explanation:

${\red{\underline{\underline{\bold{Given:-}}}}}$

• $\rm \frac{x - 4}{x - 5} + \frac{x - 6}{x - 7} = \frac{10}{3} ,$

${\blue{\underline{\underline{\bold{To\:Find:-}}}}}$

• The value of x

${\green{\underline{\underline{\bold{Solution:-}}}}}$

$\rm\implies\dfrac{x - 4}{x - 5} + \dfrac{x - 6}{x - 7} = \dfrac{10}{3}$

$\rm\implies\dfrac{(x - 4)(x - 7) + (x - 6)(x - 5)}{(x - 5)(x - 7)} \frac{10}{3}$

$\rm\dfrac{ \big\{x(x - 7) - 4(x - 7) \big \} \big\{x(x - 5) - 6(x - 5) \big \}}{ x(x - 7) - 5(x - 7)} = \dfrac{10}{3}$

$\rm\dfrac{ ({x }^{2} - 11x + 28) + ( {x}^{2} - 11x + 30) }{ {x}^{2} - 12x + 35 } = \dfrac{10}{3}$

$\implies \rm\dfrac{ {2x }^{2} - 22x + 58 }{ {x}^{2} - 12x + 35 } = \dfrac{10}{3}$

By cross multiplication :-

$\implies \rm { 3({2x }^{2} - 22x + 58) } = 10({ {x}^{2} - 12x + 35 })$

$\implies \rm { {6x }^{2} - 66 x + 174 } = { {10x}^{2} - 120x + 350 }$

$\implies \rm { {6x }^{2} { - 10x}^{2} - 66x +120x + 174 - 350 } =$

$\implies\rm { { - 4x }^{2} + 54x - 176} = 0$

$\implies - (\rm { { - 4x }^{2} + 54x - 176}) = 0$

$\implies\rm{ { 4x }^{2} - 54x + 176} = 0$

Dividing whole equation by 2

$\implies\rm2 {x}^{2} - 27x + 88 = 0$

$\implies \rm 2 {x}^{2} - 16x - 11x + 88 = 0$

$\rm \implies2x(x - 8) - 11(x - 8) = 0$

$\implies \rm(2x - 11)(x - 8) = 0$

$\boxed{ \implies \bf x = \frac{ 11}{2} \: ,\: \: 8}$