Question

pls ans fast.i will mark the correct ans as the brainliest.no spamming.​

Answer 1

SOLUTION:-

$\small \tt \: \: \frac{3}{x - 1} - \frac{2}{x - 2} = \frac{1}{x - 3} \\ \\ \small \tt \: \: \frac{3(x - 2) - 2(x - 1)}{(x - 1)(x - 2)} = \frac{1}{x - 3} \\ \\ \small\tt \: \: \frac{3x - 6 - 2x + 2}{x(x - 2) - 1(x - 2)} = \frac{1}{x - 3} \\ \\ \small \tt \: \: \frac{x - 4}{ {x}^{2} - 2x - x + 2 } = \frac{1}{x - 3} \\ \\ \small \tt \: \: \frac{x - 4}{ {x}^{2} - 3x + 2 } = \frac{1}{x - 3} \\ \\ \small \tt \: \: (x - 4)(x - 3) = {x}^{2} - 3x + 2 \\ \\ \tt \: \: x(x - 3) - 4(x - 3) = {x}^{2} - 3x + 2 \\ \\ \small \tt \: \: {x}^{2} - 3x - 4x + 12 = {x}^{2} - 3x + 2 \\ \\ \small \tt \: \: {x}^{2} - 7x + 12 = {x}^{2} - 3x + 2 \\ \\ \small \tt \: \: - 7x + 12 = - 3x + 2 \\ \\ \small \tt \: \: 7x - 3x = 12 - 2 \\ \\ \small \tt \: \: 4x = 10 \\ \\ \small \tt \: \: x = \frac{10}{4} \\ \\ \tt \: \: x = \frac{5}{2}\\ \\ \\\\ \tt \red {Explanation of steps:-} \\ \\ \texttt {\: (1) write all numerator above the least} \\ \texttt{common denominator} \\ \\ \texttt{\: (2)Remove parentheses} \\ \\ \texttt {\: (3)Collect like terms and calculate} \\ \\ \texttt {\: (4) cross multiply and eliminateghe opposite} \\ \\ \texttt{ (5) calculate and divide both the side by 4}</p><p></p><p>$

Answer 2

$\sf{\underline{\boxed{\mathbb{Solution}}}}$

➪$\dfrac{3}{x - 1} - \dfrac{2}{x - 2} = \dfrac{1}{x - 3}$

➪$\dfrac{3( x - 2) - 2 ( x - 1 )}{ ( x - 1 ) ( x - 2)} = \dfrac{1}{x - 3}$

➪$\dfrac{3x - 6 - ( 2x - 2 )}{ ( x ( x - 2) - 1( x - 2)} = \dfrac{1}{x - 3}$

➪$\dfrac{3x - 6 - 2x + 2 }{x^2 - 2x - x + 2} = \dfrac{1}{x - 3}$

➪$\dfrac{x - 4 }{ x^2 - 3x + 2 } = \dfrac{1}{x - 3}$⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

☆cross multiplication

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀➪$\dfrac{3( x - 2) - 2 ( x - 1 )}{ ( x - 1 ) ( x - 2)} = \dfrac{1}{x - 3}$

➪$( x - 4 ) ( x - 3 ) = x^2 - 3x + 2$

➪$x ( x - 3) - 4 ( x - 3 ) = x^2 - 3x + 2$

➪$x^2 - 3x - 4x + 12 = x^2 - 3x + 2$

➪$x^2 - 7x + 12 = x^2 - 3x + 2$

➪$x^2 - x^2 - 7x + 3x + 12 - 2 = 0$

➪$- 4x + 10 = 0$

➪$4x = 10$

➪$x = \dfrac{10}{4}$

➪$x = \dfrac{5}{2}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

________________________

$\sf{\underline{\boxed{\mathfrak{x = \dfrac{5}{2}}}}}$