What is the solution of (-8/2y-8)=(5/y++8/y^2-16) a) y = –4 b) y = –2 c) y = 4 d) y = 6 not b or c

D) y = 6

Step-by-step explanation:

Add the opposite of the left side:

... 0 = 8/(2y -8) +5/(y +4) -(7y +8)/(y^2 -16)

... 0 = (4(y +4) +5(y -4) -(7y +8)) / (y^2 -16) . . . . use a common denominator

... 0 = 4y +16 +5y -20 -7y -8 . . . . . multiply by (y^2 -16), eliminate parentheses

... 0 = 2y -12 . . . . . collect terms

... 0 = y -6 . . . . . . . divide by 2

... 6 = y . . . . . . . . . add 6

Comment on the solution

Keeping the expression rational and using a common denominator can avoid introducing the extraneous roots that you get when you multiply by y^2-16 at the beginning of the process. That multiplication creates a polynomial that has the roots of y^2-16 along with the solutions to the original equation.

In the above, we have a step "multiply by (y^2 -16)", but that multiplication does not have the effect of adding extraneous roots. We recognize that that step can only be valid for values of y that are not ±4. The equation itself is not defined for y = ±4. Effectively, we're ignoring the denominator and looking only for values of y that make the numerator zero.

you are playing an adventure game on your computer. you come across a troll who won't let you pass and there is no other way to get to the other side of the river except over the bridge he is guarding.

the troll is a nerd. he takes great delight in watching people struggle with his problems. very few get them. he only gives you one chance and then he changes the puzzle. you have to solve this one.

before you are four blocks. they are numbered 11,6, -7,21.

he tells that the answer he wants is minus and between -1 and - 2. you can use +, -, ×, ÷   ( and ) as many times as you like or no times at all. you don't like the way he's looking at you, but you need to cross the bridge. what do you do?