Question

solve for x: (1/x+1)+(2/x+2)=(1/x+4),x≠1,-2,-4​

Answer 1

Answer:

Consider x+11+x+22=x+44

That is, x+11=2[x+42−x+21]=2[(x+4)(x+2)2x+4−x−4]

x+21=2[(x+2)(x+4)x]

x2+6x+8=2x2+2x

Thus, we have x2−4x−8=0, which is a quadratic equation.  

(The above equation can also be obtained by taking LCM ) 

Using the quadratic formula we get, 

x=2(1)4±16−4(1)(−8)=24±48

Thus, x=2+23 or 2−23

Hence, the solution set is {2−23,2+23}

Step-by-step explanation:

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