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The number of roots of the equation ((x+...

The number of roots of the equation `((x+2)(x-5))/((x-3)(x+6))=(x-2)/(x+4)` is

A

`0`

B

`1`

C

`2`

D

`3`

Text Solution

Verified by Experts

The correct Answer is:
B
We have given `((x+2)(x-5))/((x-3)(x+6))=(x-2)/(x+4)`
`implies(x+2)(x−5)(x+4)−(x−2)(x−3)(x+6)`
`implies(x^3+x^2−22x−40)−(x^3+x^2−24x+36)=0`
`implies2x−76=0`
`impliesx=38`
Hence the number of roots are only 1.
Correct option is (b)
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