Advertisements
Advertisements
Question
Solve for x: `(3x^2 + 5x + 18)/(5x^2 + 6x + 12) = (3x + 5)/(5x - 6)`.
Advertisements
Solution
Multiplying the Numerator and Denominator of R.H.S. by -x
`(3x^2 + 5x + 18)/(5x^2 + 6x + 12) = (-3x^2 + 5)/(-5x^2 - 6)`
Since, each ratio = `"Sum of antecedents"/"Sum of consequents"`
so `(3x^2 + 5x + 18 - 3x^2 - 5x)/(5x^2 + 6x + 12 - 5x^2 - 6x)`
= `(-3x^2 - 5x)/(-5x^2 - 6x)`
`(18)/(12) = (-3x^2 - 5x)/(-5x^2 - 6x)`
⇒ `(3)/(2) = (-3x^2 - 5x)/(-5x^2 - 6x)`
⇒ `(3)/(2) = (3x + 5)/(5x + 6)`
⇒ 15x + 18 = +x + 10
⇒ 9x = -8
⇒ x = `(-8)/(9).`
APPEARS IN
RELATED QUESTIONS
Find the value of x, if: (2x + 1) : (3x + 13) is the sub-duplicate ratio of 9 : 25.
Find the triplicate ratio of the following :
`2 sqrt 5 : 5 sqrt 2`
Express the following ratios in its simplest form :
`2 1/3 : 3 1/2: 1 1/4`
If 3x – 2y – 7z = 0 and 2x + 3y – 5z = 0 find x : y : z.
Divide Rs. 720 between Sunil, Sbhil and Akhil. So that Sunil gets 4/5 of Sohil’s and Akhil’s share together and Sohil gets 2/3 of Akhil’s share.
Express the given ratio in its simplest form: 22 : 66
The ratio of the length and the width of a school ground is 5 : 2. Find the length, if the width is 40 metres.
10 boys can dig a pitch in 12 hours. How long will 8 boys take to do it?
Two numbers are in the ratio 3 : 5 and their sum is 96. The larger number is
One of the terms in a ratio cannot be 1
