SOLUTION: -3/10a^2+20a-80=a/5a-10+1/2a+8 Please show me how to solve for "a"

Question 819247: -3/10a^2+20a-80=a/5a-10+1/2a+8
Please show me how to solve for "a"
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
-3/10a^2+20a-80=a/5a-10+1/2a+8 means
That would be a weird, difficult problem.

I suspect you meant
-3/(10a^2+20a-80)=a/(5a-10)+1/(2a+8)
which you would write as

when writing on paper,
or maybe you would write it as
(It's the same, but the minus sign next to the 3 may be more convenient).
That is the problem I will solve for you.
First, you need to realize that
.
You could use as your common denominator.
(If your teacher likes that way of working through the problem, you may want to humor the teacher).
Another option is to multiply both sides of the equal sign times
.
Multiplying both sides of the equal sign times a number or expression gives you an equivalent equation,
EXCEPT if the number or expression is zero.
I would just multiply without worrying now, and later check the solutions found.

Now we have to solve that quadratic equation.
I would use factoring, starting by looking for factor pairs that multiply to give and add up to .
and so I re-write the equation as
and then factor by grouping:

and the solutions happen when
--> or
-->
Neither one of those solutions makes equal to zero,
so we should accept those solutions, but it is good to verify.
Verification:
For ,

For ,

IMPORTANT NOTE:
The long horizontal bar above is a grouping symbol.
It means that there are understood, invisible parentheses wrapping up, as separate packages,
what's on top of the line,
and whats below the line.
When typing math, you need to type those parentheses,
as required by the internationally agreed upon order of operations rules.
If you don't you will not be understood.
You probably, will get the wrong results,
and reporting wrong results will get you in trouble.
(As an analytical chemist, I know that).
(100-25)/(100+25)= ,
but if you type 100-25/100+25=
most calculators will give you the correct answer as .
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