Advertisements
Advertisements
Question
Solve the following equation by factorisation :
`(6)/x - (2)/(x - 1) = (1)/(x - 2)`
Advertisements
Solution
`(6)/x - (2)/(x - 1) = (1)/(x - 2)`
⇒ `(6x - 6 - 2x)/(x(x - 1)) = (1)/(x - 2)`
⇒ `(4x - 6)/(x^2 - x) = (1)/(x - 2)`
⇒ (4x - 6)(x - 2) = x6 - x
⇒ 4x2 - 8x - 6x + 12 = x2 - x
⇒ 4x2 - 14x + 12 - x2 + x = 0
⇒ 3x2 - 13x + 12 = 0
⇒ 3x2 - 9x - 4x + 12 = 0
⇒ 3x(x - 3) -4(x - 3) = 0
⇒ (x - 3)(3x - 4) = 0
Either x - 3 = 0,
then x = 3
or
3x - 4 = 0,
then 3x = 4
⇒ x = `(4)/(3)`
Hence x = 3, `(4)/(3)`.
APPEARS IN
RELATED QUESTIONS
Solve the following quadratic equation for x: x2 – 2ax – (4b2 – a2) = 0
Find x in terms of a, b and c: `a/(x-a)+b/(x-b)=(2c)/(x-c)`
The speed of a boat in still water is 8 km/hr. It can go 15 km upstream and 22 km downstream in 5 hours. Find the speed of the stream.
In a class test, the sum of the marks obtained by P in Mathematics and science is 28. Had he got 3 marks more in mathematics and 4 marks less in Science. The product of his marks would have been 180. Find his marks in two subjects.
Without solving the following quadratic equation Find the value of p for which the roots are equal
`px^2 - 4x + 3 = 0`
Solve the following quadratic equations by factorization:
`100/x-100/(x+5)=1`
Solve the following quadratic equations by factorization:
`5/(x - 2) - 3/(x + 6) = 4/x`
Three consecutive natural numbers are such that the square of the first increased by the product of other two gives 154. Find the numbers.
Car A travels ‘x’ km for every litre of petrol, while car B travels (x + 5) km for every litre of petrol.
- Write down the number of litres of petrol used by car A and car B in covering a distance of 400 km.
- If car A uses 4 litres of petrol more than car B in covering 400 km. write down an equation, in A and solve it to determine the number of litres of petrol used by car B for the journey.
In the centre of a rectangular lawn of dimensions 50 m × 40 m, a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be 1184 m2 [see figure]. Find the length and breadth of the pond.
