Advertisements
Advertisements
Question
Solve the following equation:
`1/("x - 1") + 2/("x" - 2) = 3/("x" - 3)`
Advertisements
Solution
`1/("x - 1") + 2/("x" - 2) = 3/("x" - 3)`
`= (1("x" - 2) + 2("x" - 1))/(("x" - 1)("x" - 2)) = 3/("x" - 3)`
`=> ("x" - 2 + 2"x" - 2)/("x"^2 - "2x" - "x" + 2) = 3/"x - 3"`
`=> (3"x" - 4)/("x"^2 - "3x" + 2) = 3/"x - 3"`
⇒ (x - 3)(3x - 4) = 3(x2 - 3x + 2)
⇒ 3x2 - 4x - 9x + 12 = 3x2 - 9x + 6
⇒ 3x2 - 13x - 3x2 + 9x = 6 - 12
⇒ - 4x = - 6
x = `(-6)/(-4) = 3/2 = 1 1/2`
APPEARS IN
RELATED QUESTIONS
A rectangle’s length is 5 cm less than twice its width. If the length is decreased by 5 cm and width is increased by 2 cm; the perimeter of the resulting rectangle will be 74 cm. Find the length and width of the origi¬nal rectangle.
A man’s age is three times that of his son, and in twelve years he will be twice as old as his son would be. What are their present ages.
A man completed a trip of 136 km in 8 hours. Some part of the trip was covered at 15 km/hr and the remaining at 18 km/hr. Find the part of the trip covered at 18 km/hr.
The present age of a man is twice that of his son. Eight years hence, their ages will be in the ratio 7 : 4. Find their present ages
Solve: `("6x" + 1)/2 + 1 = ("7x" - 3)/3`
A man sold an article for ₹ 396 and gained 10% on it. Find the cost price of the article
The numerator of a fraction is 5 less than its denominator. If 3 is added to the numerator, and denominator both, the fraction becomes`4/5`. Find the original fraction.
Given that x ≥ y. Fill in the blank with suitable inequality sign
x – y `square` 0
Linear inequation has almost one solution
Solve the following inequation
x ≤ 7, where x is a natural number
