+7 the negative reciprocal of the sum of all values of x that satisfy the equation x-sqrt(x+1)/x+sqrt(x+1)=11/5
Below is my steps but idk if its right
36x2 (x to the power of 2) =162 (16 to the power of 2) (x+1)
and then the 16 to the power of to eventually equals 256x+256
+6252 I assume this is (parens are your friend)x−√x+1x+√x+1=115
Let's pull a bit of a trick herea=√x+1x−ax+a=1155x−5a=11x+11a6x+16a=03x=−8a=−8√x+1
9x2=64(x+1)9x2−64x−64=0Using the quadratic formula, (which I leave to you)x=8, −98Since we squared the equation we must check these roots
x=8⇒a=38−38+3=511≠1158 is a extraneous solutionx=−89⇒a=13−89−13−89+13=115so x=−89 is an actual root, and the only one
−1−89=98
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