Question

Please help! #2a and #2b

Answer 1

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

x = 1

Hope my answer helps!