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
Solve the following equation:
`("x" - 1)/("7x" - 14) = ("x" - 3)/("7x" - 26)`
Fifteen less than 4 times a number is 9. Find the number.
Fifteen more than 3 times Neetu’s age is the same as 4 times her age. How old is she ?
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.
The difference of two numbers is 3 and the difference of their squares is 69. Find the numbers.
If the same number be added to the numbers 5, 11, 15 and 31, the resulting numbers are in proportion. Find the number.
Solve: `1/3"x" - 6 = 5/2`
Solve:
`1/10 - 7/x = 35`
Solve: `"x" + 7 - "8x"/3 = "17x"/6 - "5x"/8`
Solve the following inequalities
4n + 7 ≥ 3n + 10, n is an integer
