Advertisements
Advertisements
Question
Solve the following equation by using formula :
`(2)/(x + 2) - (1)/(x + 1) = (4)/(x + 4) - (3)/(x + 3)`
Solution
`(2)/(x + 2) - (1)/(x + 1) = (4)/(x + 4) - (3)/(x + 3)`
`(2x + 2 - x - 2)/((x + 2)(x + 1)) = (4x + 12 - 3x - 12)/((x + 4)(x + 3)`
⇒ `x/((x + 2)(x + 1)) = x/((x + 4)(x + 3)`
⇒ `(1)/((x + 2)(x + 1)) = (1)/((x + 4)(x + 3)` ...[Dividing by x if x ≠ 0]
⇒ `(1)/(x^2 + 3x + 2) = (1)/(x^2 + 7x + 12)`
⇒ x2 + 7x + 12 – x2 – 3x – 2 = 0
⇒ 4x + 10
⇒ 2x + 5 = 0
⇒ 2x = –5
⇒ x = `(-5)/(2)`
If x = 0, then
`(0)/((x + 2)(x + 1)) = (0)/((x + 4)(x + 3)`
Which is correct
Hence x = 0, `(-5)/(2)`.
APPEARS IN
RELATED QUESTIONS
Check whether the following is quadratic equation or not.
`sqrt(3x^2)-2x+1/2=0`
Solve : x(x – 5) = 24
Solve `9/2 x = 5 + x^2`
`6x^2+x--12=0`
`sqrt3x^2-2sqrt2x-2sqrt3=0`
`9x^2+6x+1=0`
`2x^2+ax-a^2=0`
`x/(x-1)+x-1/4=4 1/4, x≠ 0,1`
If -1 and 3 are the roots of x2+px+q=0
then find the values of p and q
Solve:
`1/(18 - x) - 1/(18 + x) = 1/24` and x > 0
