how do you simplify equations?

5/36 + 9/ 28
= 30/252 + 81/252
= 111/252
= 37/84


x^2 - 2x-15/ x^2 - 25
= (x-5)(x+3)/(x+5)(x-5)
= (x+3)/(x+5)

For the first you have to have a common denominator and express each term in those terms. First find the common denominator:

It so happens that 36 and 28 are both factors of 1008if you multiply them together.

36 goes into 1008 28 times so the first term is:

(5 times 28)/1008 or 140/1008

and 28 goes into 1008 36 times so the second term is:

(9 times 36)/1008 or 324/1008

Adding the two gives: 464/1008

Both numerator and denominator can be divided by 16 to give:

29/63

For the second, each expression needs to be expressed in (a+b) terms.

The numerator factors to (x-5)(x+3) and the denominator factors to
(x+5)(x-5)

Thus you have (x-5)(x+3)/(x+5)(x-5)

(x-5)/x-5) is 1 so the expression simplifies to (x+3)/(x+5)

1)
Find the LCM of 36 and 28:
36 = 2^2 * 3^2
28 = 2^2 ........* 7
-------------------------------
....= 2^2 * 3^2 * 7
....= 252

5/36 + 9/28
= (5 * 7)/(36 * 7) + (9 * 9)/(28 * 9)
= 35/252 + 81/252
= (35 + 81)/252
= 116/252
= 29/63

========================

2)
(x^2 - 2x - 15)/(x^2 - 25)
= (x^2 + 3x - 5x - 15)/(x^2 - 5^2)
= [(x^2 + 3x) - (5x + 15)]/[(x + 5)(x - 5)]
= [x(x + 3) - 5(x + 3)]/[(x + 5)(x - 5)]
= [(x + 3)(x - 5)]/[(x + 5)(x - 5)]
= (x + 3)/(x + 5)

1) 19/63
2) (x+3)/(x+5)

I'm not sure if you wrote down the equation properly
do you mean...
(x^2-2x-15)/(x^2-25)
(x^2-2x-15)/(x^2)-25
x^2-(2x-15)/(x^2-25)
x^2-(2x-15)/(x^2)-25
x^2-2x-15/x^(2-25)
or x^2-2x-15/x^(2)-25
In any case to simplify you simply bring it into the form ax^2+bx+c=0
I'm assuming you meant the first case since it's the simplest
in which case...

0.46x^2-11.51=x^2-2x-15
0.54x^2-2x-3.49=0
to solve the equation enter it into the formula (-b+and-sqrt(b^2-4ac))/2a
so x1= ((-2)+sqrt(2^2-4*0.54*(-3.49))/2*.54=1.3
x2= -2-sqrt...=-5

these are the problems in which the foremost step to be taken is taking l.c.m. (lowest common diviser ) of the denominators of the whole equation
for e.g.
l.c.m. of 5/36 + 9/28denominators i.e.28,36 is 252
now divide the l.c.m by denominator and multiply the numerator by the quotient and the follow the operation sign which is + in this case so the eq becomes
35+81/252 = 116/252 is the ans

now the second eq
l.c.m. is x^2-25
now next step is
(x^2)*(x^2 -25)-(2x-15)/x^2-25
=x^(2+2)-25x^2-2x-15/x^2-25
=x^4-25^2-2x-15/x^2-25 is the ans

140+324/1008=464/1008=29/63
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(x-5)(x+3)/(x-5)(x+5)=(x+3)/(x+5)