Rational Equations?

Question

I have no clue how to solve these..

5/x+2=6/x

x+4=-4/x


Help would be very much aprecciated.

Answer 1

1. *Eliminate fractions > multiply the denominator by everything >

x(5/x) + x(2) = x(6/x)

First: cancel "like" terms >

5 + 2x = 6

Sec: combine "like" terms > subtract 5 from both sides >

5 - 5 + 2x = 6 - 5
2x = 1

Third: solve for "x" by isolating it on one side > divide both sides by 2 >

2x/2 = 1/2
x = 1/2

2. Follow the same format as number (1) :-)

Answer 2

OK first you need to multiply x on both sides to distribute on one side and cancell om the other

x(5/x +2) = x(6/x) = 5+2x =6

Set everything thats not x to the right then divide by 2
2x=1 = x = 1/2

For the second equation you multiply by x on both sides as well to cancell
x(x+4)= x(-4/x) = (x^2+4x = -4) = x^2+4x+4

You can use the quadratic equation but a simpler way would be to factor out the polynimial

x^2+4x+4 = (x+2)(x+2)

Then setting each factor to 0 you find that x = -2

x+2=0 , x+2=0

x=-2 , x=-2

Answer 3

5/x+2=6/x
let t = 1/x
5t +2 = 6t <=> t = 2 <=> 1/x = 2 <=> x = 1/2

x+4=-4/x
<=> x^2 + 4x = -4 and x <> 0
<=> (x + 2)^2 = 0 and x <> 0
<=> x = -2

Answer 4

For both questions, start by multiplying both sides by x, giving:

5 + 2x = 6
x^2 + 4x = -4

For the first question, subtract 5 from both sides, giving 2x =1. Then divide both sides by 2, giving x=1/2 as the answer.

For the second question, add 4 to both sides, to get x^2 + 4x + 4 = 0. Then you have to notice that this factorizes to give (x+2)^2 = 0. Taking the square root gives x+2 = 0, since the only number whose square is zero is zero. Then subtract 2 from both sides to give x = -2 as the answer.

Answer 5

Let's look at the first one.

5/x + 2 = 6/x

The first thing you need to do is clear the denominators. So multiply both sides by x. Then you have

5 + 2x = 6
2x = 1
x = 1/2

Use the same approach for the second question.

Answer 6

u hv to mulitply both sides of the equal sign with x.

5/x+2=6/x
5+2x=6
2x=1
x=1/2


x+4=4/x
x^2+4x-4=0
for this question, use the quadratic equation to solve it.