SOLUTION: {{{ sqrt(2x)- sqrt(x+1) =3/sqrt(x+1) }}}.

Algebra ->  Radicals -> SOLUTION: {{{ sqrt(2x)- sqrt(x+1) =3/sqrt(x+1) }}}.      Log On


   

Question 958933: +sqrt%282x%29-+sqrt%28x%2B1%29+=3%2Fsqrt%28x%2B1%29+.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%282x%29-3%2Fsqrt%28x%2B1%29=sqrt%28x%2B1%29

sqrt%282x%28x%2B1%29%29-3=sqrt%28%28x%2B1%29%28x%2B1%29%29

%28sqrt%282x%5E2%2B2%29-3%29%5E2=%28x%2B1%29%28x%2B1%29

%282x%5E2%2B2%29-6sqrt%282x%5E2%2B2%29%2B9=x%5E2%2B2x%2B1

-6sqrt%282x%5E2%2B2%29=x%5E2%2B2x%2B1-2x%5E2-2-9

-6sqrt%282x%5E2%2B2%29=-x%5E2%2B2x-10

6sqrt%282x%5E2%2B2%29=x%5E2-2x%2B10

36%282x%5E2%2B2%29=%28x%5E2-2x%2B10%29%5E2, easier to use a lattice multiplication method for the right hand side. Continue from there.

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

+sqrt%282x%29-+sqrt%28x%2B1%29+=3%2Fsqrt%28x%2B1%29+.
sqrt%282x%29+%2A+sqrt%28x+%2B+1%29+-+%28sqrt%28x+%2B+1%29+%2A+sqrt%28x+%2B+1%29%29+=+3 -------- Multiplying by LCD, sqrt%28x+%2B+1%29

sqrt%282x%28x+%2B+1%29%29+-+%28x+%2B+1%29+=+3

sqrt%282x%5E2+%2B+2x%29+-+x+-+1+=+3

sqrt%282x%5E2+%2B+2x%29+=+3+%2B+x+%2B+1

sqrt%282x%5E2+%2B+2x%29+=+x+%2B+4

%28sqrt%282x%5E2+%2B+2x%29%29%5E2+=+%28x+%2B+4%29%5E2 ------- Squaring both sides

2x%5E2+%2B+2x+=+x%5E2+%2B+8x+%2B+16

2x%5E2+-+x%5E2+%2B+2x+-+8x+-+16+=+0

x%5E2+-+6x+-+16+=+0

(x - 8)(x + 2) = 0

highlight_green%28x+=+8%29		OR	 	x = - 2(ignore)