Cannot solve Math equation containing fractions, please help!?

Question

Equation = 4/x + 2/x+1 = 5

I know we have to clear the fraction with the LCD and I try multiplying each side by x(x+1) but am not getting the answer the book says of x=1 or x=-4/5. If someone could show me step - by step, it would be so helpful!! THANK YOU!

Thank you James I finally get it, yes!!!

Thank you April that was really detailed i appreciate it, it really helped!!

Answer 1

So multiply both sides by x(x+1) and you get 4(x+1)+2x=5x(x+1)
so 4x+4+2x=5x^2+5x
so 5x^2-x-4=0
(5x+4 )(x-1)=0
so x=-4/5 or x=1

Answer 2

I am assuming the problem is:

4/x + 2/(x+1) = 5... that is, that this is a binomial on the left side, right???

The lcd is x(x+1) so everything is multiplied by it to get rid of the demonimator.

by placing this in the numerator of all three terms (the two on the left and the 5) and then canceling within each term you get.

4(x+1) + 2x = 5x(x+1) follow so far? Then distribute. If I lost you, let me know....

4x +4 +2x = 5x^2 + 5x Collect like terms and set to zero.
-5x^2 +x +4 = 0 Did you get this. If not you made some mistakes in getting it set up to zero.

But this is not in standard form so you must multiply everything by -1 because the x^2 term must be positive.

5x^2 - x -4 = 0.... when the trinomial has 2 minus signs, one of the factor is + and the other -

( + ) ( - ) I always set these up first so I don't have to mess with it later. Then put in what you know, and that is that x is the first term in each ( )

( x+ )( x - ) Now your job is to find the combination of 5 and 4 that will get you that negative 1x in the center of the trinomial. It is called foil, and your book may show you how to do that.

(5x+4)( x- 1) = 0 can you finish it from here? If not, or I lost you or you have other problems, write.

Answer 3

If x has two values, then you have to simplify your equation into a quadratic equation in order to get two values of x.

First, rewrite the equation:
4/x + 2/x+1 = 5

Then, make the denominators same. In this case, it's x² + x:
4(x + 1)/x(x + 1) + 2(x)/(x + 1)(x) = 5
(4x + 4) / (x² + x) + 2x/ x² + x = 5
(4x + 4 + 2x) / (x² + x) = 5

After that, shift (x² + x) to the RHS:
(4x + 4 + 2x) = 5(x² + x)

Then, solve the addition on the LHS and factorization on the RHS:
6x + 4 = 5x² + 5x

After that, form a quadratic equation:
0 = 5x² + 5x - 6x - 4
5x² - x - 4 = 0

Finally, factorize it and find the values of x:
(x - 1)(5x + 4) = 0

x - 1 = 0
x = 1

OR

5x + 4 = 0
x = -(4/5)

Thus, x = 1, -4/5 (final answer)

Answer 4

a million. use x yand z and make an equation x=6+y z=3(x+y)-4 then the glaring one x+y+z=a hundred and eighty z=3(6+y+y)-4 z=14+6y 6+y+y+14+6y=a hundred and eighty 8y=a hundred and sixty y=20 x=26 z=134 2. x+y=ninety x=30+y 30+y+y=ninety 2y=60 y=30 x=60 3. w=2x x=2y y=2z w+x+y+z=360 sustitute a uncomplicated variable x=4z w=8z 8z+4z+2z+z=360 15z=360 z=24 y=40 8 x=ninety six w=192 4. x+x-4>0 x>2 x+x-4+x+x=seventy 5 4x=seventy 9 x=19.seventy 5 then i think of the question is calling to apply the inequalities to make a nother one for the achieveable lenghts. so 2

Answer 5

4/x + 2/x= 5-1
4/x + 2/x = 4
6/x=4
6=4x
6/4=x
3/2=x or 1.5= x

Plug it back into the formula and you will find it works
Good luck