# Solve the Following Equation: 1/("X + 6") + 2/("X" - 2) = 3/("X" - 3) - Mathematics

Sum

Solve the following equation:

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

#### Solution

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

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

=> ("x" - 2 + 2"x" - 2)/("x"^2 - "2x" - "x" + 2) = 3/"x - 3"

=> (3"x" - 4)/("x"^2 - "3x" + 2) = 3/"x - 3"

⇒ (x - 3)(3x - 4) = (x2 - 3x + 2)

⇒ 3x2 - 4x - 9x + 12 = 3x2 - 9x + 6

⇒ 3x2 - 13x - 3x2 + 9x = 6 - 12

⇒ -4x = -6

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

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#### APPEARS IN

Selina Concise Mathematics Class 8 ICSE
Chapter 14 Linear Equations in one Variable
Exercise 14 (A) | Q 21 | Page 166