Algebra Help?

Question

Would you please explain the answer of this problem to me.

x/ x - 5 + x + 1/ x + 5

remember to make the denominators common. thanks

Answer 1

x / (x - 5) + 1 / (x + 5)
[ x (x + 5) + 1 (x - 5) ] / [ (x - 5) (x + 5) ]
[ x² + 6x - 5 ] / [ (x - 5) (x + 5) ]

Answer 2

I suspect the actual problem is

x/(x-5) + 1/(x+5)

you need to have a common denominator; the best way to do this easily is to multiply the first fraction by (x+5)/(x+5) which is actually multipling it by 1; similarly multiply the second fraction by (x-5)/(x-5). This makes the common denominator (x+5)(x-5) and the problem quickly becomes

[x(x+5) +(x-5)]/[(x+5)(x-5)] =

[x^2 +5x +x -5]/[(x+5)(x-5)] =

[x^2 +6x -5]/[(x+5)(x-5)] =
[x^2 + 6x -5}/[x^2 - 25]

Answer 3

i'm assuming you meant x/(x-5) +x +1/(x+5)

your common denominator is going to be (x-5)(x+5)
You need to multiply top and bottom of each part of this equation by whichever parts of the common denominator the numerator lacks.

so you'll end up with
x(x+5)/(x+5)(x-5) + x(x+5)(x-5)/(x+5)(x-5) + (X-5)/(x+5)(x-5)

combine the numerators so you have

x(x+5)+x(x+5)(x-5)+(x-5) / (x+5)(x-5)

then simplify

x^2+5x+x^3-25x+x-5 / x^2-25

then order the numerator

x^3+x^2-24x-5 / x^2-25

that is as far as i can go with it. Good luck

Answer 4

only an equation can be solved. An equation contains an equal sign. This can be reduced to:

1-5+x+1/x+5 or 1+x+1/x or x+x^2+1

Answer 5

Thats the whole key to this problem COMMON DENOMINATORS. In this case the LCD is (x+5)(X-5). from there you cross multiply. This is a vital concept to your success in math.

I'll do a sample problem

X/Y + Y/X

LCD = XY

Answer 6

can you go and add more info for me?
on here we didnt know which one on the numerator or denominator.

can you include the parentheses like
x/(x-5) that mean you said x-5 is on the bottom or if you mean x+1 is on the top so (x+1)

so i can help you , plz add more

if you meant
x/(x-5) +(x+1)/(x+5) then LCD is (x-5)(x+5)

x(x+5) - (x+1)(x-5)
--------------------------
(x-5)(x+5)

x^2 +5x -(x^2-5x+x-5)
-----------------------------
x^2 -25

x^2+5x-(x^2-4x-5)
------------------------
x^2-25

x^2+5x-x^2+4x+5
-----------------------
x^2-25

9x+5
------------
x^2-25