abysmal at maths- please help with this equation due in for tomorrow?

Question

14/a+1 + 8/a-2 =4

gcse maths homework- confused.com!
any help greatly appreciated as it will save me from a detention for lack of homework! =)

Sorry forgot to say, though you have probably already guessed-I have to solve the equation ( am also meant to show steps as to how i got the final answer)

Answer 1

They give detention for lack of homework? Wow.. How school has changed. :) I added comments in for each step so hopefully you can understand how we arrive at the solution.

14/a + 1 + 8/a - 2 = 4
14/a + 8/a -1 = 4 (We've just taken our constants (+1 and -2) and subtracted 1-2 to get -1)
14/a + 8/a (1-1)= 4 +1 (add one to both sides of the equation)
14/a + 8/a = 5
22/a = 5 (since the demoninators remain the same, we may add the numerators)
22/a * a = 5 * a (multiple both sides by A)
22 = 5a Now just solve for A
A = 22/5

Lenpol: You shifted your -2a to a +2 during the second step. Can't do that. :)

Answer 2

Should read as :-
14/(a+ 1) + 8/(a -2) = 4

Multiply both sides by (a + 1) (a - 2):-
14(a - 2) + 8(a + 1) = 4(a -2) (a + 1)
14a - 28 + 8a + 8 = 4 (a² - a - 2)
22a - 20 = 4a² - 4a - 8
0 = 4a² - 26a + 12
2a² - 13a + 6 = 0
(2a - 1) (a - 6) = 0
a =1/2 or a = 6

Answer 3

You probably left out the parentheses and the problem should look like this, 14/(a+1) + 8/(a-2) = 4
Multiply everything by (a+1)(a-2)
(a+1)(a-2)(14/(a+1)) + (a+1)(a-2)(8/(a-2)) = 4(a+1)(a-2)
14(a-2) + 8(a+1) = 4(a^2 - 2a +a - 2)
14a - 28 + 8a + 8 = 4(a^2 - a - 2)
22a - 20 = 4a^2 - 4a - 8
Subtract 22a and add 20 to each side
0 = 4a^2 - 26a + 12
Divide everything by 2
0 = 2a^2 - 13a + 6
Factor
0 = (2a-1)(a-6)
2a - 1 = 0 or a - 6 = 0
a = 1/2 or a = 6

Answer 4

14/a + 1 + 8/a - 2 = 4
mutli. everything by a so the division goes away
A(14/a + 1 + 8/a - 2 = 4) ---> 14 + 1(a) + 8 - 2(a) = 4(a)
now u have to get all of the a's to one side so subtract the 1(a) and add the 2(a) so they are all on the right side and add the 14 and 8
14 + 8 = 5(a) ---> 22=5(a)
now divide 5 on both sides and you get what a is equal to
22/5 ---> 4.4 = a
if u put it bak into the equation, it comes out correct

Answer 5

a=4.4
move whole numbers right so +1 becomes 4-1 then becomes 4-1+2(5)
ignore the a`s so, 14+8=5,22=5 ,then divide 22 by 5 to give you the value of a

Answer 6

You'll be able to visualize this better if you multiply everything by a. This changes your expression to:

14 + a + 8 - 2a = 4a

From there it is pretty simple, just group everything and solve for a. You should get a = 22/5

By the way, anyone who can spell "abysmal" and use it correctly in a sentence can't be too bad in math :)

Answer 7

I think what you're asking is:
14/(a+1) + 8/(a-2) = 4

the brackets are important!

first thing you need to do is combine the two fractions. So we need to get the bit on the bottom the same.

14(a-2)/(a+1)(a-2) + 8(a+1)/(a-2)(a+1) = 4
[14(a-2) +8(a+1)]/(a+1)(a-2) = 4

now... i'm going to multiply both sides by (a+1)(a-2) that will reduce the chances of me mistyping my fractions!
14(a-2)+8(a+1) = 4(a+1)(a-2)

multiply out all the brackets
14a-28+8a+8 = 4a^2+4a-8a-8
combine like terms
22a-20 = 4a^2-4a-8
move everything over to the same side
0 = 4a^2 -26a +12

and then you can use whatever your favourite method is to solve the quadratic equation, giving a = 6 or 0.5

Now, its worth plugging both of these numbers into the original equation, to check they work:
first, a=6
14/(6+1)+8/(6-2) = 14/7 + 8/4 = 2 + 2 = 4
next, a=0.5
14/(0.5+1)+8/(0.5-2) = 14/1.5 + 8/-1.5 = 9.333 - 5.333 = 4

And we're done

Answer 8

We can combine the fractions since they have
the same denominator:
22/a + 1 -2 = 4.
This gives
22/a -1 = 4.
Add 1 to each side:
22/a = 5
Multiply both sides by a:
22 = 5a
Divide by 5:
a = 22/5.
Hope that saves you from detention.
Suggest you go over these steps again,
so you can do this type of problem on your own!

Answer 9

a = 6

Answer 10

assuming (a+1) is entirely under 14 and (a-2) is entirely under 8, the answer to this equation is

(13 +/- sqrt(57)) / 4

if that is not the case and only a is underneath 14 and 8 (which is actually how you typed it), then the answer to the equation is

22/5 = 4.4