Advertisements
Advertisements
Question
Solve the following equation by factorization
`a/(ax - 1) + b/(bx - 1) = a + b, a + b ≠ 0, ab ≠ 0`
Advertisements
Solution
`a/(ax - 1) + b/(bx - 1) = a + b, a + b ≠ 0, ab ≠ 0`
⇒ `(a/(ax - 1) - b) + (b/(bx - 1) - a)` = 0
⇒ `(a - abx + b)/((ax - 1)) + (b - abx + a)/((bx - 1))` = 0
⇒ `(a + b - abx) [1/(ax - 1) + 1/(bx - 1)]` = 0
⇒ `(a + b - abx) [(bx - 1 + ax - 1)/((ax - 1)(bx - 1))]` = 0
⇒ `((a + b - abx)(ax + bx - 2))/((ax - 1)(bx - 1)` = 0
⇒ `(a + b - abx) (ax + bx - 2)` = 0
⇒ Either a + b - abx = 0,
then a+ b = abx
x = `(a + b)/(ab)`
or
ax + bx - 2 = 0,
then x(a + b) = 2
x = `(2)/(a + b)`
Hence x = `(a + b)/(ab), (2)/(a + b)`.
APPEARS IN
RELATED QUESTIONS
Find two numbers whose sum is 27 and product is 182.
In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects
The length of a hall is 5 m more than its breadth. If the area of the floor of the hall is 84 m2, what are the length and breadth of the hall?
The area of a right angled triangle is 165 m2. Determine its base and altitude if the latter exceeds the former by 7 m.
The sum of natural number and its positive square root is 132. Find the number.
Solve the following equation: c
Solve the following equation:
`("x" + 1)/("x" - 1) - ("x" - 1)/("x" + 1) = 5/6 , "x" ≠ -1,1`
Solve the following equation: a2b2x2 + b2x - a2x - 1 = 0
Solve equation using factorisation method:
`(x - 3)/(x + 3) + (x + 3)/(x - 3) = 2 1/2`
A train, travelling at a uniform speed for 360 km, would have taken 48 minutes less to travel the same distance if its speed were 5 km/h more. Find the original speed of the train.
