Question

Help please! detailed would be great!

Answer 1

The goal here is to lose all those denominators so we can solve for y.  The common is found by first factoring everything that can be factored  2y-8 factors to 2(y-4) and y^2-16 factors to (y-4)(y+4).  The GCF then we will use for cancellation of the denominators is 2(y-4)(y+4).  The first term there, when multiplied by that GCF, will cancel with 2(y-4), leaving us with -8(y+4), no more denominator.  Going to the next term, when we multiply by the GCF the cancellation happens with the (y+4) term leaving us with no denominator anymore and 2*5(y-4), which simplifies to 10(y-4).  Last term.  The cancellation happens with the (y+4)(y-4), leaving us with 2(7y+8).  Putting all that together looks like this now: -8(y+4)=10(y-4)-[2(7y+8)].  Distributing gives us -8y-32=10y-40-[14y+16]  which simplifies to -8y-32=10y-40-14y-16.  We will combine like terms to get 0=4y-24.  We can factor out the 4 to get 4(y-6)=0.  Now of course 4 doesn't equal 0, but y - 6 = 0 and y = 6.  Last choice above.  There you go!