Home
Class 10
MATHS
Simplify (1)/( (x+1) (x+2) ) + (1)/( (x+...

Simplify `(1)/( (x+1) (x+2) ) + (1)/( (x+2) (x+3)) + (1)/( (x+3) (x+1))`

A

`(1)/((x +1) (x+3))`

B

`(2)/( (x+1) (x+3))`

C

`(3)/( (x+2) (x+3))`

D

`(3)/((x+1) (x+3))`

Text Solution

AI Generated Solution

The correct Answer is:
To simplify the expression \[ \frac{1}{(x+1)(x+2)} + \frac{1}{(x+2)(x+3)} + \frac{1}{(x+3)(x+1)}, \] we will follow these steps: ### Step 1: Identify the Least Common Multiple (LCM) The denominators of the three fractions are \((x+1)(x+2)\), \((x+2)(x+3)\), and \((x+3)(x+1)\). The LCM of these denominators is \[ (x+1)(x+2)(x+3). \]
Promotional Banner

Topper's Solved these Questions

  • ALGEBRAIC EXPRESSIONS

    CENGAGE|Exercise TEST YOURSELF GAME TIME (Illustrated Puzzles)|3 Videos

  • ALGEBRAIC EXPRESSIONS

    CENGAGE|Exercise TEST YOURSELF (Multiple Choice Questions)|20 Videos

  • AREA OF A TRIANGLE

    CENGAGE|Exercise OLYMPIAD AND NTSE LEVEL EXERCISES |10 Videos

Similar Questions

Explore conceptually related problems

Simplify: (5x+3)(x-1)(3x-2)

Simplify: (3x-2)(x-1)(3x+5)

Solvef or x,(1)/((x-1)(x-2))+(1)/((x-2)(x-3))+(1)/((x-3)(x-4))=(1)/(6)

Simplify : ((1)/(2)x(1)/(4))+((1)/(2)x6)

Solve for x : (1)/((x-1)(x-2))+(1)/((x-2)(x-3))+(1)/((x-3)(x-4))=(1)/(6)

Simplify (x^(2)-1)/(x+1)-:(x^(3)-1)/(x^(2)+x+1)

Simplify: (3)/(2)x^(2)(x^(2)-1)+(1)/(4)x^(2)(x^(2)+x)-(3)/(4)x(x^(3)-1)