Question

Help! need step by step to understand

4x/9 + x-10/9

t^2+6t/t-1 - 7/t-1

3/x + 13/x-11

5/4x^2y - y/ 14xz

x^2+2x/12x+54 - 3x/8x+36

2/x^2+8x+15 + 1/x^2+11x+30

Answer 1

you should use parentheses
x - 10/9 means \( x - \frac{10}{9}\)
but you probably mean
(x-10)/9 which means \( \frac{x-10}{9} \)

Answer 2

if two fractions have the same denominator, you add the tops, and the bottom stays the same

example:
\[ \frac{1}{4} + \frac{2}{4} = \frac{1+2}{4} = \frac{3}{4} \]
this rule works for letters
Example:
\[ \frac{x}{a} + \frac{2y}{a} = \frac{x+2y}{a} \]

Answer 3

for that i got 5x+10/9?

Answer 4

first, use parens

2nd, how did the -10 change to +10 ?

Answer 5

i meant 5x-10/9

Answer 6

you meant
(5x-10)/9

both the 5x and the -10 are being divided by 9

Answer 7

yes. so thats my final answer since its just simplifying right?

Answer 8

what did you get for the 2nd question ?

Answer 9

(t+7)

Answer 10

\[ \frac{t^2+6t-7}{t-1} \]
but you can factor the top into (t+7)(t-1)
so this is
\[ \frac{(t+7)(t-1)}{t-1} = t+7 , t≠1\]

Answer 11

for the 3rd question you need a common denominator. in this case x(x-11) is the smallest common denominator

Answer 12

okay. for the third i got (16x-33)/x^2-11x

Answer 13

yes, but I would type it
(16x-33)/(x^2-11x)

because that whole mess (x^2-11x) is in the bottom

It looks like you know what you are doing.

Answer 14

the only real problem im having is number 6. can you help me with that?

Answer 15

the 4th question also needs a common denominator

try 4*14*x^2*y*z

Answer 16

can you help with 6? @phi

Answer 17

\[ \frac{2}{x^2+8x+15}+ \frac{1}{x^2+11x+30}\]
I assume you know how to factor these? if not see
http://www.khanacademy.org/math/trigonometry/polynomial_and_rational/quad_factoring/v/factoring-quadratic-expressions

you get
\[ \frac{2}{(x+3)(x+5)}+ \frac{1}{(x+5)(x+6)}\]
the common denominator will be (x+3)(x+5)(x+6)

that means multiply the first fraction by (x+6)/(x+6)
and multiply the 2nd fraction by (x+3)/(x+3)

can you finish ?