Solve this Rational Problem! | Quick & Easy Explanation

#OlympiadMathematics #OlympiadPreparation #CollegeEntranceExam

[Skank_and_Gutterboy]

This is a nice problem. I took the approach of solving the equation for y directly: y = -4x/(x-4). Then in the large expression, I substituted in -4x/(x-4) anywhere that a y appears, so now it's only in terms of x. It simplifies down so that all of the x's cancel and you're left with -2, which is the answer. That was probably the hard way to do it but it worked.

[dicksonphisthur]

I'm a 69 year old American living in Tokyo and I really enjoy watching these videos.

[devondevon]

Answer = -2
Nice solution.
Luckily, I recall that 1/3 - 1/4 = 1/12 from solving for sin 15 degrees or sin pie/12 (sin pie/12= sin pie/3 - sin pie/4, the sine difference formulae) hence 1/3 - 1/12 = 1/4, which is in the same form, as 1/x- 1/y = 1/4, therefore x=3 and y=12. Then I plugged in the values of x and y into
2x-2y-3xy = 6-24-108 = -126 AND
x- y+ x y = 3-12+72 = 63 -126/63 = -2 Answer. Notwithstanding, great explanation.

[HappyFamilyOnline]

Very well explained👍
Thanks for sharing😊😊

[srividhyamoorthy]

I just came back from school and am here to check out your vids 😀😀

[illyriumus]

Used the same method but instead of replacing XY, I found x-y and plugged the values. Easier and quicker.

[skoijlg]

Divide by x y the numerator and the denominator. In the numerator we get -3.5, and in the denominator 1.75.

[mikoliism]

I pulled -xy from the numerator and xy from the denominator and that gave me the 1/x-1/y on the top and bottom that I could replace with 1/4 the rest was just fraction addition and subtraction

[burlfromlondon]

Can reduce the number of steps by just factoring out y-x rather than distributing the numeric multiplers. At a later step you aleady assume that y-x is not zero

[math]

a lot of algebra bro, love it, thanks for sharing

[petergriff]

y-x/xy =1/4
y-x=1 or x-y=-1
xy=4
Putting it in given equation we get result -2

[nirupamasingh]

V nice question. Can it be also solved by dividing num and denom by xy?

[luis]

If (y-x)/xy=1/4 then x-y=-1 and xy=4 is a possible solution. I replaced the two directly in the second expression, getting -2 also. There are infinite pairs of x, y satisfying the first expression. In particular y=2, 568 and x=1, 568 makes (y-x)=1 and xy=4.

[prabhuenrichexcell]

3/4 - 1/2 = 1/4
Take x = 4/3 and y = 2
Substitute in the equation you get -2

[kafaichan]

xy = 4(y-x), subst back into the expression, ans = -2

[susennath]

Sorry to interrupt.

Pls divide both by XY and accumulate Sig wise you will get the answer in two lines

[humester]

This way may be easier
(1/x) – (1/y) = 1/4
(y - x) / (xy) = 1/4
Therefore, (x - y) = -1 and xy = 4
and so, [2x - 2y - 3xy] / [x - y + 2xy]

= [2(-1) - 3(4)] / [(-1) + 2(4)] = (-2 - 12)/(-1 + 8) = - (14/7) = - 2

[mathswan]

Divide both denominator and numerator by xy

[girolamocapita]

Easy :you have to divide each member for xy and then reckon the result

[isimsoyisim]

y-x =1 and xy=4. By this way solving is easy. After only a few seconds you can find - 2