Advertisements
Advertisements
Question
Solve the following equation: `1/("x" - 1) + 2/("x" - 1) = 6/"x" , (x ≠ 0)`
Advertisements
Solution
`1/("x" - 1) + 2/("x" - 1) = 6/"x" , (x ≠ 0)`
`(("x" - 1) + 2 ("x" - 2))/(("x" - 2)("x" - 1)) = 6/"x"`
x(x + 1) + 2x(x - 2) = 6(x - 2)(x - 1)
x2 - x + 2x2 - 4x = 6(x2 - 2x - x + 2)
3x2 - 5x = 6x2 - 18x + 12
3x2 - 13x + 12 = 0
`"x"^2 - 13/3 "x" + 4 = 0`
`"x"^2 - 3"x" - 4/3 "x" + 4 = 0`
`"x"("x" - 3) - 4/3 ("x" - 3) = 0`
`("x" - 3)("x" - 4/3) = 0`
x = 3 , x = `4/3`
APPEARS IN
RELATED QUESTIONS
John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. We would like to find out how many marbles they had to start with.
The sum of two numbers is 8 and 15 times the sum of their reciprocals is also 8. Find the numbers.
An aeroplane left 50 minutes later than its scheduled time, and in order to reach the destination, 1250 km away, in time, it had to increase its speed by 250 km/hr from its usual speed. Find its usual speed.
Solve : x2 – 11x – 12 =0; when x ∈ N
Solve the following quadratic equation by factorisation.
2y2 + 27y + 13 = 0
If 2 is a root of the equation x2 + bx + 12 = 0 and the equation x2 + bx + q = 0 has equal roots, then q =
Solve the following equation: `("a+b")^2 "x"^2 - 4 "abx" - ("a - b")^2 = 0`
The sum of the square of 2 consecutive odd positive integers is 290.Find them.
A rectangle of area 105 cm² has its length equal to x cm. Write down its breadth in terms of x. Given that the perimeter is 44 cm, write down an equation in x and solve it to determine the dimensions of the rectangle.
A man spent Rs. 2800 on buying a number of plants priced at Rs x each. Because of the number involved, the supplier reduced the price of each plant by Rupee 1.The man finally paid Rs. 2730 and received 10 more plants. Find x.
