Question

1/x+1 + 1/x+5 = 1/x+2 + 1/x+4​

Answer 1

Answer:

There are multiple ways of solving this.

You can directly solve for x:

Answer⤵⤵

Cross multiply to get,

x + 4 = x(x+1)

x^2 - 4 = 0

(x-2)(x+2) = 0

x = 2 or -2

Though a much faster approach would be to use the options.

You can see that x cannot be 0/-1/-4 because then one of the terms will have 0 in the denominator. A fraction cannot have 0 in the denominator hence x must be either -2 or -3.

Put x = -2 and check:

1 - (1/2) = 1/2

1/2 = 1/2

So x = -2 satisfies and hence, is the answer.

Answer 2

Answer:

There are multiple ways of solving this.

You can directly solve for x:

Answer⤵⤵

Cross multiply to get,

x + 4 = x(x+1)

x^2 - 4 = 0

(x-2)(x+2) = 0

x = 2 or -2

Though a much faster approach would be to use the options.

You can see that x cannot be 0/-1/-4 because then one of the terms will have 0 in the denominator. A fraction cannot have 0 in the denominator hence x must be either -2 or -3.

Put x = -2 and check:

1 - (1/2) = 1/2

1/2 = 1/2

So x = -2 satisfies and hence, is the answer.

hope it helps you✌✌..