Solve these below:?

Question

1. 5/x = 3/2

2. [ x / ( x - 2 )] – [ 5 / x ] = 3 / 4

3. ( a – 2 ) / ( a² - 4 ) = 1

4. (2x – 4 ) / 2x = ( 3x – 6 ) / 3x

5. 1 / r = 1 / s + 1 / t Solve for s.

6. W = a² / t Solve for t.

Answer 1

Ok…I’ve got them all here now…sorry it took me so long!

1. 5/x = 3/2 (cross-multiply)
3x = 10 (divide both sides by 3 to get…)
X = 3.33 (rounded to 2 decimal places)

2. [ x / ( x - 2 )] – [ 5 / x ] = 3 / 4 (combine the denominators on the left side of the equation by multiplying the fraction…..[ x / ( x - 2 )]…..by x/x and the other fraction….[ 5 / x ]…..by (x – 2)/(x – 2) so that the denominators will be the same).
[x^2 / (x^2 – 2x)] – [(5x – 10)/ (x^2 – 2x)] = ¾ (now u have the same denominators…combine the two fractions on the left hand side of the equation together.)
[x^2 – 5x + 10]/[x^2 – 2x] = ¾ (cross-multiply)
4x^2 – 20x + 40 = 3x^2 – 6x (combine like terms together)
x^2 – 14x + 40 = 0 (now, u get a quadratic equation…so u have to factor this into 2 sets of factors.)
(x - 10)(x - 4) = 0 (set each factor to 0)
x – 10 = 0 and x – 4 = 0
x = 10 and x = 4 (these are your 2 solutions)

3. ( a – 2 ) / ( a² - 4 ) = 1 (factor the ( a² - 4 ) into (a+2) and (a-2) then u can cancel out the (a-2) in the denominator with the (a-2) in the numerator)
1/ (a + 2) = 1 (cross-multiply)
a + 2 = 1 (subtract 2 from both sides)
a = -1

4. (2x – 4 ) / 2x = ( 3x – 6 ) / 3x --- I think this question has been mistyped…coz I don’t see any logical way of working this out…

5. 1 / r = 1 / s + 1 / t Solve for s. (rewrite the equation like this)
1/s = 1/r – 1/t (now, multiply the fraction…1/r…by t/t, and the fraction…1/t…r/r so that the denominators will be the same.)
1/s = t/rt – r/rt (now combine the 2 fractions on the right hand side of the equation together)
1/s = (t – r)/ rt (cross-multiply)
s (t – r) = rt (divide both sides by (t – r)
s = rt / (t – r)

6. W = a² / t Solve for t. (re-write this equation as Wt = a²)
Wt = a² (then divide both sides by W to get…)
t = a² / W

…and btw, if u don’t understand how I factored that…just post in the additional info spot that u didn’t understand how to factor it…hope this helps! =D

Answer 2

1. 3x=10
x=10/3

2. [x²-5(x-2)]/x(x-2) = 3/4
x²-5x+10/x(x-2) = 3/4
4(x²-5x+10) = 3x(x-2)
4x²-20x+40 = 3x² -6x
4x²-20x+40=3x²+6x = 0
x²-14x+40 = 0
(x-10)(x-4) = 0
x=10,4

3. (a-2)/(a+2)(a-2) = 1
1/(a+2) =1
(a+2) = 1
a=-1

4. 3x (2x-4) = 2x (3x-6)
6x²-12x = 6x² - 12x
no solution

5. 1/r = t+s/st
st = r(t+s)
st = rt+rs
st=rs = rt
s(t-r) = rt
s = rt/t-r

6. Wt = a²
t = a²/W

Answer 3

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Answer 4

5/x = 3/2

2x(5/x) = 2x(3/2)

10 = 3x

10 / 3 = 3x / 3

10/3 = x

3 1/3 = x

- - - - - - - - -s-

Answer 5

to me, that just looks like a bunch of numbers and letters mixed up!!! i have no idea how to do that.