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# Solve the Following Equation: - Mathematics

Sum

Solve the following equation :

1/(("x" - 1)(x - 2)) + 1/(("x" - 2)("x" - 3)) + 1/(("x" - 3)("x" -4)) = 1/6

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#### Solution

1/(("x" - 1)(x - 2)) + 1/(("x" - 2)("x" - 3)) + 1/(("x" - 3)("x" -4)) = 1/6

(("x" -3)("x" - 4) + ("x" - 1)("x" - 4) + ("x" - 1)("x" - 2))/(("x" - 1)("x" - 2)("x" - 3)("x" - 4)) = 1/6

("x"^2 - 3"x" - 4"x" + 12 + "x"^2 - "x" - 4"x" + 4 + "x"^2 - "x" - 2"x" + 2)/(("x" - 1)("x" - 2)("x" - 3)("x" - 4)) = 1/6

(3"x"^2 - 15 "x" + 18)/(("x" - 1)("x" - 2)("x" - 3)("x" - 4)) = 1/6

(3("x"^2 - 5"x" + 6))/(("x" - 1)("x" - 2)("x" - 3)("x" - 4)) = 1/6

(3("x" - 3)("x" - 2))/(("x" - 1)("x" - 2)("x" - 3)("x" - 4)) = 1/6

3/(("x" - 1)("x" - 4)) = 1/6

x2 - 5x+ 4= 18

x2 - 5x - 14= 0

x2 + 2x - 7x -14= 0

x( x+ 2) - 7(x + 2)= 0

(x + 2)(x - 7) =  0

x = -2, x = 7

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#### APPEARS IN

Frank ICSE Class 10 Mathematics Part 2
Chapter 6 Quadratic Equations
Exercise 6.1 | Q 27
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