Advertisements
Advertisements
Question
Solve the following equation :
`("x" - 1)/("x" - 2) + ("x" - 3)/("x" - 4) = 3 1/3`
Advertisements
Solution
`("x" - 1)/("x" - 2) + ("x" - 3)/("x" - 4) = 3 1/3`
`(("x" - 1)("x" - 4) + ("x" - 3)("x" - 2))/(("x" - 2)("x" - 4)) = 10/3`
`("x"^2 - 5"x" + 4 + "x"^2 - 5"x" + 6)/("x"^2 - 6"x" + 8) = 10/3`
`(2"x"^2 - 10"x" + 10)/("x"^2 - 6"x" + 8) = 10/3`
6x2 -30x+ 30 = 10x2 - 60x + 80
4x2 - 30x + 50 = 0
2x2 - 15x + 25 = 0
`"x"^2 - 15/2 "x" + 25/2 = 0`
`"x"^2 -5"x" - 5/2 "x" + 25/2 = 0`
`"x" ("x" - 5) - 5/2 ("x" - 5) = 0`
`("x" - 5)("x" - 5/2) = 0`
x = 5 , x = `5/2`
APPEARS IN
RELATED QUESTIONS
Solve the following quadratic equation by Factorisation method: x2 + 7x + 10 = 0
A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.
Solve the following quadratic equations by factorization:
a(x2 + 1) - x(a2 + 1) = 0
A train covers a distance of 90 km at a uniform speed. Had the speed been 15 km/hour more, it would have taken 30 minutes less for a journey. Find the original speed of the train.
Solve the following quadratic equations by factorization:
`(x-3)/(x+3 )+(x+3)/(x-3)=2 1/2`
The area of a right-angled triangle is 600 cm2. If the base of the triangle exceeds the altitude by 10 cm, find the dimensions of the triangle.
Solve equation using factorisation method:
`5/("x" -2) - 3/("x" + 6) = 4/"x"`
In each of the following determine whether the given values are solutions of the equation or not.
6x2 - x - 2 = 0; x = `-(1)/(2), x = (2)/(3)`
In each of the following, determine whether the given values are solution of the given equation or not:
x2 - 3`sqrt(3)` + 6 = 0; x = `sqrt(3)`, x = -2`sqrt(3)`
In each of the following, determine whether the given values are solution of the given equation or not:
`x = 1/x = (13)/(6), x = (5)/(6), x = (4)/(3)`
