Question

Solve the equation for x:
1/x+1 +2/x+2 = 7/x+5, x≠-1,-2,-5

Answer 1

Step-by-step explanation:

1/x + 1 + 2/x + 2 = 7/x +5

1/x + 2/x -7/x = 5 - 2 - 1

(1 + 2 - 7)/x = 2

-4/x = 2

-4 = 2x

x = -4/2

x = -2

Answer 2

The value of x is 1 and -1.5.

Step-by-step explanation:

Consider the given equation is

$\dfrac{1}{x+1}+\dfrac{2}{x+2}=\dfrac{7}{x+5}$

Multiply both sides by (x+1)(x+2)(x+5).

$\left(x+2\right)\left(x+5\right)+2\left(x+1\right)\left(x+5\right)=7\left(x+1\right)\left(x+2\right)$

$x^2+7x+10+2x^2+12x+10=7x^2+21x+14$

$3x^2+19x+20=7x^2+21x+14$

$3x^2+19x+20-7x^2-21x-14=0$

$-4x^2-2x+6=0$

Divide both sides by -2.

$2x^2+x-3=0$

Splitting the middle term we get

$2x^2+3x-2x-3=0$

$x(2x+3)-1(2x+3)=0$

$(2x+3)(x-1)=0$

Using zero product property we get

$x=-\dfrac{3}{2},1$

Therefore, the value of x is 1 and -1.5.

#Learn more

Solve the equation (2+x)(7-x)/(5-x)(4+x)=1​.

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