Advertisements
Advertisements
Question
Solve the following equation by factorization
`(x + 2)/(x + 3) = (2x - 3)/(3x - 7)`
Advertisements
Solution
`(x + 2)/(x + 3) = (2x - 3)/(3x - 7)`
(x + 2) (3x - 7) = (2x - 3) (x + 3)
⇒ 3x2 - 7x + 6x - 14 = 2x2 + 6x - 3x - 9
⇒ 3x2 - x - 14 = 2x2 + 3x - 9
⇒ 3x2 - x - 14 - 2x2 - 3x + 9 =0
⇒ x2 - 4x - 5 = 0
⇒ x2 - 5x + x - 5 = 0
x(x - 5) + 1(x - 5) = 0
⇒ (x - 5) (x + 1) = 0
Either x - 5 = 0,
then x = 5
or
x + 1 = 0,
then x = -1
Hence x = 5, -1.
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.
Some students planned a picnic. The budget for food was Rs. 500. But, 5 of them failed to go and thus the cost of food for each member increased by Rs. 5. How many students attended the picnic?
Solve:
x(x + 1) + (x + 2)(x + 3) = 42
`2x^2+5x-3=0`
Solve the following quadratic equation by factorisation.
3x2 - 2√6x + 2 = 0
Solve the following quadratic equations by factorization: \[\frac{16}{x} - 1 = \frac{15}{x + 1}; x \neq 0, - 1\]
Solve the following equation: 4x2 - 13x - 12 = 0
Solve the following equation: `"a"/("x" - "a") + "b"/("x" - "b") = (2"c")/("x" - "c")`
Solve the equation x4 + 2x3 - 13x2 + 2x + 1 = 0.
Solve the following equation by factorization
2x2 – 9x + 10 = 0,when x∈Q
