Question

Solve by using the LCD. 4/x-5 + 1/x = x-1/x-5

(please help!!)

Answer 1

See attachment for math work and answer.

Reject x = 5.

Answer is x = 1.

Answer 2

Answer: x ≠ 5; x≠ 0

`(4)/(x-5)+(1)/(x)=(x-1)/(x-5)\\\\<=> (4x+x-5)/(x(x-5))=(x(x-1))/(x(x-5)) \\<=> 4x+x-5=x(x-1)\\<=> 5x-5 = x^(2)-x\\<=> x^(2) -6x+5=0\\<=>(x-5)(x-1)=0\\`

because x≠ 5 => x - 5 ≠ 0

=> x - 1 = 0

⇔ x = 1

Explanation: