math help, simplifying completely anyone good at this stuff?

Question

1. x^2/ x^2-25 plus 7x+10/x^2-25

2. 3x+5/ x+3 minus x-1/x+3

3. 2x/x-3 minus 6/x-3

4. 2x+1/x-3 plus x+2/3-x

5. 2x+1/3 plus -x+2/3

6. 4-x/x-9 minus 3x-8/9-x

7. 2/x minus 1/x = x/ 3x+10

8. x/8 = 1/ x+2

9. x= 5/ 6-x

10. 8/ y-3 = 6/y+4

Answer 1

1. x^2/ (x^2-25) + (7x+10)/(x^2-25)

Same LCD, so add numerators

(x^2 + 7x + 10)/(x^2 - 25)

Factor the numerator and denominator to see if any cancellation can be done

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

(x + 2)/(x - 5)

2. (3x+5)/(x+3) - (x-1)/(x+3)

Again, same LCD, so do the arithmetic

(3x + 5 - x + 1)/(x + 3)

(2x + 6)/(x + 3)

2(x + 3)/(x + 3)

2

4. (2x+1)/(x-3) + (x+2)/(3-x)

Here you need to notice that (3 - x) = - (x - 3)

(2x+1)/(x-3) - (x+2)/(x - 3))

(2 x + 1 - x - 2)/(x - 3)

(x - 1)/(x - 3)

7. 2/x - 1/x = x/(3x+10)

Now it appears you want to solve an equation.

1/x = x/(3x + 10) {combine like terms

Note that the LCD of the fractions is x(3x + 10)

Multiply both sides by the LCD to clear the denominators of the fractions

1/x = x/(3x + 10)

3x + 10 = x^2

x^2 - 3x - 10 = 0

(x - 5)(x + 2) = 0

x = 5, x = -2

Answer 2

so, what? you are expecting someone to do your whole assignment for you?

half of these already have two fractions with the same denominator. Why haven't you already done those at least?

1. (x^2+7x+10)/(x^2-25)
factor the numerator and denominator and simplify if possible.
do any of the factors of 10 add up to 7?
factors of 10: 1*10, 2*5, -1*-10, -2*-5
5+2=7
(x+5)(x+2)/(x+5)(x-5) since (x+5)/(x+5)=1
(x+5)(x+2)/(x+5)(x-5)=(x+2)/(x-5)

if the denominator isnt the same you make it the same by changing the fraction(s) necessary to the least common denominator. notice that (x-a)=(-1)(a-x)

7. 2/x - 1/x = x/(3x+10)
(2-1)/x = x/(3x+10)
1/x = x/(3x+10)
multiply the left by (3x+10)/(3x+10) multiply the right by x/x
1(3x+10)/x((3x+10) = x*x/x(3x+10)
once the denominator is the same, the expressions are equal if the numerators are equal
NOTICE: the denominator can not equal zero, so
x can not = 0, and x can not = -10/3

3x+10=x^2
x^2-3x-10=0
are there factors of -10 that add up to -3?
factors of -10: -1*10, -2*5, -5*2, -10*1
-5+2 = -3
x^2-3x-10=(x-5)(x+2)=0
x=-2, x=5

Answer 3

And you were assigned exactly ten problems for homework, right?

Answer 4

okay i do not have time leaving back to answer later

























































































































not really