Question

Find x....


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Answer 1

Answer:

$\tt\large \: your \: ans = \frac{ - 20}{3}$

Step-by-step explanation:

$\sf\ \frac{1}{x + 1} + \frac{2}{x + 2} = \frac{3}{x - 14} \\ \\ \sf\ \implies: \frac{1 \times (x + 2) + 2 \times (x + 1)}{(x + 1)(x + 2)} = \frac{3}{x - 14} \\ \\ \sf\ \implies: \frac{x + 2 + 2x + 2}{ {x}^{2} + 2x + x + 2} = \frac{3}{x - 14} \\ \\ \sf\ \implies: \frac{x + 2x + 4}{ {x}^{2} + 3x + 2 } = \frac{3}{x - 14} \\ \\ \sf\ \implies:x - 14(3x + 4) = 3( {x}^{2} + 3x + 2) \\ \\ \sf\ \implies: {3x}^{2} - 56 = {3x}^{2} + 9x + 4 \\ \\ \sf\ \implies: \cancel{{3x}^{2} } \cancel{- {3x}^{2} }- 56 - 4 = 9x \\ \\ \sf\ \implies: - 60 = 9x \\ \\ \sf\ \implies: \frac{ - 60}{9} = x \\ \\ \boxed{\sf\ x\implies: \frac{ - 20}{3} }$

Answer 2

Answer:

1

+

x+2

2

=

x−14

3

⟹:

(x+1)(x+2)

1×(x+2)+2×(x+1)

=

x−14

3

⟹:

x

2

+2x+x+2

x+2+2x+2

=

x−14

3

⟹:

x

2

+3x+2

x+2x+4

=

x−14

3

⟹:x−14(3x+4)=3(x

2

+3x+2)

⟹:3x

2

−56=3x

2

+9x+4

⟹:

3x

2

−3x

2

−56−4=9x

⟹:−60=9x

⟹:

9

−60

=x

x⟹:

3

−20