Expert: Sherman D. - 4/20/2004

Question
Thanks for your help, my teacher needs us to study for two quizes this week, and one has problems like these, can you please explain and answer as usual?

simplify expression
x-4 2x+4
___+____
9x    9x

Add expression

2     3
___+____
x+8 x-6

simplify expression

1+4
 _
 7
___
1-4
 _
 3

simplify expression

2 1
_+__

x 3x
_____

4    3
___+__
3x   2x

perform operations and simplify

3x+4     2
______-____
x^2-16   x-4

simplify expression

1
___=1
x-4 _
     4
_____
-1
__-6 =  
16
x     __
      1

simplify expression

-2x+7   -2x-7
_____+______
24x     24x

Add expression

 5        7
______+_____
6(x+2)  6(x+2)

again thanks a lot for your time

Answer
Next time, could you please type it like i do, so that i can understand it better.

((x - 4)/(9x)) + ((2x + 4)/(9x))
Same denominator
((x - 4) + (2x + 4))/(9x)
(x - 4 + 2x + 4)/(9x)
((1 + 2)x + (-4 + 4))/(9x)
(3x)/(9x)
(3/9) * (x/x)
(1/3) * 1
Ans : (1/3)

-----------------------------------------------------------

(2/(x + 8)) + (3/(x - 6))
Multiply by (x + 8)(x - 6)
((2(x-6))/((x+8)(x-6))) + ((3(x+8))/((x+8)(x-6)))
((2x - 12)/((x + 8)(x - 6))) + ((3x + 24)/((x + 8)(x - 6)))
Same denominator
((2x - 12) + (3x + 24))/((x + 8)(x - 6))
((2 + 3)x + (-12 + 24))/((x + 8)(x - 6)))
(5x + 12)/((x + 8)(x - 6))
(5x + 12)/(x^2 - 6x + 8x - 48)
Ans : (5x + 12)/(x^2 + 2x - 48)

-----------------------------------------------------------

If by this you mean

((1 + 4)/7) / ((1 - 4)/3)
(5/7)/(-3/3)
(5/7)/(-1)
(5/7)/(-1/1)
Multiply top half by reciprocal of bottom half
(5/7) * (1/-1)
Multiply across
(5/-7)
or
Ans : (-5/7)

-----------------------------------------------------------

If by this you mean

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

Then we can first work the numerator and denominator separately first.

(2/x) + (1/(3x))
Multiply by 3x
((2 * 3)/(3x)) + (1/(3x))
(6/(3x)) + (1/(3x))
same denominator
(6 + 1)/(3x)
Ans : (7/(3x))


(4/(3x)) + (3/(2x))
Muliply by 6x
((4 * 2)/(6x)) + ((3 * 3)/(6x))
(8/(6x)) + (9/(6x))
Same Denominator
(8 + 9)/(6x)
Ans : 17/(6x)

Now we have

(7/(3x)) / (17/(6x))

Multiply top half by reciprocal of bottom half

((7/(3x))) * ((6x)/17)
Multiply across
(42x)/(51x)
(42/51) * (x/x)
(14/17) * 1
Ans : (14/17)

-----------------------------------------------------------

((3x + 4)/(x^2 - 16)) - (2/(x - 4))
((3x + 4)/((x - 4)(x + 4))) - (2/(x - 4))
Multiply by (x - 4)(x + 4)
((3x + 4)/((x - 4)(x + 4))) - ((2(x + 4))/((x - 4)(x + 4)))
((3x + 4)/((x - 4)(x + 4))) - ((2x + 8)/((x - 4)(x + 4)))
Same Denomiator
((3x + 4) - (2x + 8))/((x - 4)(x + 4))
(3x + 4 - 2x - 8)/((x - 4)(x + 4))
((3 - 2)x + (4 - 8))/((x - 4)(x + 4))
(x + (-4))/((x - 4)(x + 4))
(x - 4)/((x - 4)(x + 4))
((x - 4)/(x - 4)) * (1/(x + 4))
1 * (1/(x + 4))
Ans : 1/(x + 4)

-----------------------------------------------------------

Didn't come out right. You can retype it for me if you like. For ex: if your problem is suppose to be a fraction divided by another fraction, then you would right your problem like this

((n1)/(d1))/((n2)/(d2)) = ((n3)/(d3))/((n4)/(d4))
Making sure to put each value in ().

1
___=1
x-4 _
   4
_____
-1
__-6 =
16
x    __
   1

-----------------------------------------------------------

((-2x + 7)/(24x)) + ((-2x - 7)/(24x))
Same denominator
((-2x + 7) + (-2x - 7))/(24x)
(-2x + 7 - 2x - 7)/(24x)
((-2 - 2)x + (7 - 7))/(24x)
((-2 + (-2))x + 0)/(24x)
(-4x)/(24x)
(-4/24) * (x/x)
(-1/6) * 1
Ans : (-1/6)

-----------------------------------------------------------

(5/(6(x + 2))) + (7/(6(x + 2)))
Same denominator
(5 + 7)/(6(x + 2))
12/(6(x + 2))
(12/6) * (1/(x + 2))
2 * (1/(x + 2))
Ans : 2/(x + 2)