Question

solve for x:x-1/x-2+x-3/x-4 =31/3(x=/2,4)​

Answer 1

$\huge{\underline{\underline{\textsf{\textbf{Solution}}}}}$

Question:

Solve for $x:$ $\frac{x - 1}{x-2} + \frac{x - 3}{x-4} = 3\frac{1}{3}$

Answer:

Given equation is $\frac{x - 1}{x-2} + \frac{x - 3}{x-4} = 3\frac{1}{3}$

Multiplying both the sides by 3, we get:

$\implies{3(x-1)(x-4) + 3(x-3)(x-2)}$

$\implies{10(x-4)(x-2)}$

$3(x² - 5x + 4)+3(x²-5x+6) = 10(x²-6+8)$

$3x² - 15x + 12 + 3x² - 15x + 18 = 10x² - 60x + 8$

$\implies{6x² - 30x + 30 = 10x² - 60x + 8}$

$\implies{-4x²+30x - 50 = 0}$

$\implies{2x² - 15x + 25 = 0}$

$\implies{2x² - 10x - 5x + 25 = 0}$

$\implies{2x(x - 5) - 5(x - 5) = 0}$

$\implies{(x - 5) (2x - 5) = 0}$

$\implies{x - 5 = 0 \: \: and \: \: 2x - 5 = 0}$

$\implies{x = 5, x = \frac{5}{2}}$

Hence, $\bold{x = 5, \frac{5}{2}}$ are the required solutions.

----------------------------------

Answer 2

Answer:

Solution

Question:

Solve for x : 2²=2+³=3²

Answer:

Given equation is + ² = 3²

Multiplying both the sides by 3, we get:

→ 3(x - 1)(x-4) + 3(x − 3)(x - 2)

10(x-4) (x - 2)

3(x²5x + 4) + 3(x² - 5x + 6) 10 (268)

=

3x²15x + 12 + 3x2 - 15x + 18 = 10x2 60x + 8

6x2 30x30 10x² 60x + 8

-4x² + 30x50= 0

⇒ 2x²15x + 25 = 0

2x² 10x 5x + 250

→ 2x(x - 5) - 5(x - 5) = 0

⇒ (x - 5)(2x - 5) = 0

⇒ x 5 = 0 and 2x5=0

5 ⇒ x = 5, x = 131202

Hence, x = 5, are the required solutions.

Step-by-step explanation: