Answer:
x = 5, x = [tex]\frac{5}{2}[/tex]
Step-by-step explanation:
Given
[tex]\frac{x-1}{x-2}[/tex] + [tex]\frac{x-3}{x-4}[/tex] = 3 [tex]\frac{1}{3}[/tex]
[tex]\frac{(x-1)(x-4)+(x-3)(x-2)}{(x-2)(x-4)}[/tex] = [tex]\frac{10}{3}[/tex]
[tex]\frac{x^2-5x+4+x^2-5x+6}{x^2-6x+8}[/tex] = [tex]\frac{10}{3}[/tex]
[tex]\frac{2x^2-10x+10}{x^2-6x+8}[/tex] = [tex]\frac{10}{3}[/tex] ( cross- multiply )
10(x² - 6x + 8) = 3(2x² - 10x + 10) ← distribute both sides
10x² - 60x + 80 = 6x² - 30x + 30 ← subtract 6x² - 30x + 30 from both sides
4x² - 30x + 50 = 0 ( divide through by 2 )
2x² - 15x + 25 = 0 ← in standard form
(2x - 5)(x - 5) = 0 ← in factored form
Equate each factor to zero and solve for x
2x - 5 = 0 ⇒ 2x = 5 ⇒ x = [tex]\frac{5}{2}[/tex]
x - 5 = 0 ⇒ x = 5
Answer:
Step-by-step explanation:
x-1/x-2+x-3/x-4=31/3
3(x²-4x-x+4)+3(x²-2x-3x+6)=31(x²-4x-2x+8)
3(x²-5x+4)+3(x²-5x+6)=31(x²-6x+8)
3x²-15x+12+3x²-15x+18=31x²-186x+248
3x²+3x²-31x²-15x-15x+186x+12+18-248=0
-25x²+156x-218=0
-(25x²-156+218)=0
By using quadratic equation
