Advertisements
Advertisements
Question
Solve the following equation: `("x" + 3)/("x" + 2) = (3"x" - 7)/(2"x" - 3)`
Advertisements
Solution
`("x" + 3)/("x" + 2) = (3"x" - 7)/(2"x" - 3)`
(x + 3)(2x - 3) = (3x - 7)(x + 2)
2x2 + 6x - 3x - 9 = 3x2 - 7x + 6x - 14
2x2 + 3x - 9 = 3x2 - x - 14
(3 - 2)x2 +(-1 - 3) x + (- 14 + 9) = 0
x2 - 4x -5= 0
x2 + x - 5x - 5 = 0
x (x+ 1) - 5 (x + 1) = 0
( x + 1)(x - 5) = 0
(x+ 1)= 0, (x - 5)= 0
X = -1 , x = 5
APPEARS IN
RELATED QUESTIONS
The difference of squares of two number is 88. If the larger number is 5 less than twice the smaller number, then find the two numbers.
The hypotenuse of a right triangle is 25 cm. The difference between the lengths of the other two sides of the triangle is 5 cm. Find the lengths of these sides.
If −5 is a root of the quadratic equation\[2 x^2 + px - 15 = 0\] and the quadratic equation \[p( x^2 + x) + k = 0\] has equal roots, find the value of k.
Solve the following equation: 4x2 - 13x - 12 = 0
Three consecutive natural numbers are such that the square of the first increased by the product of other two gives 154. Find the numbers.
Solve the following equation by factorization
`x/(x - 1) + (x - 1)/x = 2(1)/(2)`
Solve the following equation by factorization
`(x + 1)/(x - 1) + (x - 2)/(x + 2)` = 3
Solve the following equation by factorization
`(1)/(x - 3) - (1)/(x + 5) = (1)/(6)`
Mohini wishes to fit three rods together in the shape of a right triangle. If the hypotenuse is 2 cm longer than the base and 4 cm longer than the shortest side, find the lengths of the rods.
A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.
