Hey there!!
( a ) 1 + 3/x²-1 = 2/x-1
x²-1+3/x²-1 = 2/x-1
x²+2/x²-1 = 2/x-1
Note : we can write x²-1 as (x-1)(x+1)
I wrote this with the identity a²-b² = (a+b)(a-b)
x²+2/(x-1)(x+1) = 2/x-1
Multiplying (x-1)(x+1) on both sides
x²+2 = 2(x-1)(x+1) / (x-1)
x²+2 = 2(x+1)
x²+2 = 2x+2
x²-2x = 0
x(x-2)=0
x=0
x-2=0
x=2
x = 0 and 2
( b ) ( √x+3 ) - 1 = x
√x+3 = x+1
x+3 = ( x+1)²
x+3 = x²+2x+1
x+3-x²-2x-1=0
-x+2-x²=0
-x²-x+2=0
x = -b plus or minus √b2 -4ac / 2a
x = -1 plus or minus √ 1 + 8 / 2
-1 plus or minus √9 / 2
-1 plus or minus 3/2
-1 +3 / 2
x = 1
-1 - 3 / 2
-4/2
x = -2
negative cannot be a value
Hence, the answer is
Hope my answer helps!
