Maths question Please Help !!!?

Question

whats :

3/ x-5 + 1/ x-1


(algebraic fraction, you can see it http://www.gcsemathspastpapers.com/images/p5j01q52.gif )

Thanks in advance !

Answer 1

For simplification, you want to make this into one fraction. To do so, you must find a common denominator, that is, an expression which is both a multiple of (x-5) and (x-1). Because these two have no common factors, we simply multiply them.

The denominator will therefore become (x-5).(x-1); in the first fraction both sides are multiplied with (x-1), in the second fraction, with (x-5):

... 3(x-1) / (x-5)(x-1) + 1(x-5) / (x-5)(x-1)

Because the two fractions now have the same denominator, you can add the numerators:

... [ 3(x-1) + 1(x-5) ] / (x-5)(x-1)

Expand the products in the numerator:

... [ 3x - 3 + x - 5 ] / (x-5)(x-1)

and combine like terms for the final answer:

... (4x - 8) / (x - 5)(x - 1)

(Btw, MamaMia made a little mistake here: -3 - 5 = -8, not -2.)

And if you want to expand the denominator as well:

... (4x - 8) / (x^2 - 6x + 5)

Answer 2

Get a common denominator.

Multiply the first term by (x-1)/(x-1)
Mutliply the second term by (x-5)/(x-5)

(3)(x - 1) / (x-5)(x-1) + (1)(x-5) / (x-1)(x-5) =

(3x -3) / (x-5)(x-1) + (x - 5) / (x-5)(x-1)

= (3x - 3 + x - 5) / (x-5)(x-1)

= (4x - 2) / (x-5)(x-1)

= (4x - 2) / (x² - 6x + 5)

Answer 3

3/ (x-5) + 1/ (x-1)

Multiply numerator and denominator by (x-5)(x-1)


3(x-5)(x-1)/ (x-5)(x-1)(x-5) + (x-5)(x-1)/ (x-5)(x-1)(x-1)

Simplify
3(x-1)/ (x-1)(x-5) + (x-5)/ (x-5)(x-1)

(3(x-1)+ (x-5))/ (x-5)(x-1)

(4x-8)/ ((x-5)(x-1))

4(x - 2)/ ((x - 5)(x - 1))
.

Answer 4

Dear,
Lets be sraight to solve this problem.

3/(x-5) + 1/(x-1)

3(x-1) + 1(x-5)
-------------------------
(x-5)(x-1)

3x-3+x-5
--------------------------
x(x-1) - 5(x-1)

4x-8
-------------------------
x^2-x-5x+5

4(x - 2)
------------------------
x^2-6x+5

And thats It!!