Question

Solve the equation and verify your answer:

(x² – (x+1) (x+2))/(5x+1) = 6

Answer 1

We have,

(x² – (x+1) (x+2))/(5x+1) = 6

By cross-multiplying we get,

(x² – (x+1) (x+2)) = 6(5x+1)

x² – x² – 2x – x – 2 = 30x + 6

-3x – 2 = 30x + 6

30x + 3x = -2 – 6

33x = -8

x = -8/33

Now let us verify the given equation,

(x² – (x+1) (x+2))/(5x+1) = 6

By substituting the value of ‘x’ we get,

((-8/33)² – ((-8/33)+1) (-8/33 + 2))/(5(-8/33)+1) = 6

(64/1089 – ((-8+33)/33) ((-8+66)/33)) / (-40+33)/33) = 6

(64/1089 – (25/33) (58/33)) / (-7/33) = 6

(64/1089 – 1450/1089) / (-7/33) = 6

((64-1450)/1089 / (-7/33)) = 6

-1386/1089 × 33/-7 = 6

1386 × 33 / 1089 × -7 = 6

6 = 6

Hence, the given equation is verified.