add x/ x+3 + 6/x+5

Question

adding    x/x+3 + 6/x+5

 

Answer 1

Gayla:

Assuming your expression is intended to be x/(x+3)+6/(x+5), you can perform the following steps to combine terms:

1st, get both terms to have the same denominator.  You can do this by multiplying the 1st term by (x+5)/(x+5), since (x+5) is the denominator of the 2nd term.  Similarly, you can multiply the 2nd term by (x+3)/(x+3).  This results in ((x)(x+5))/((x+3)(x+5)) + ((6)(x+3))/((x+5)(x+3))

Next, since both terms now have the same denominator of (x+3) (x+5), you can combine the numerators as, follows:  ((x)(x+5) + (6)(x+3))/((x+5)(x+3)) = (x²+5x+6x+18)/((x+5)(x+3)) = (X²+11x+18)/((x+5)(x+3))

You can then factor the numerator to get ((x+2)(x+9))/((x+5)(x+3))

Admittedly, this can be confusing with the keyboard, due to all of the parentheses.

George T.

Answer 2

(x+9)(x+2) / (x+3)(x+5)

Answer 3

Assumption: Directions for your homework state something like, "Simplify the expression."

Assumption: The problem actually reads, "x/(x+3)+6/(x+5)".

1.) You must always find the LCD when adding fractions.

What is the LCD of this expression? Typically you can play it safe and just say that it's the product of the two denominators (which it usually is).

The LCD is (x+3)(x+5).

2.) Rewrite both fractions in terms of the LCD:

[x(x+5)]/[(x+3)(x+5)]+[6(x+3)]/(x+3)(x+5)

3.) Add the two fractions:

[x(x+5)+6(x+3)]/[(x+3)(x+5)]

 

4.) Expand the numerator (or both the numerator and denominator):

x²+5x+6x+18 = x²+11x+18

 

Answer:

[x²+11x+18]/[(x+3)(x+5)]

 

Answer 4

Rationalize the denominator, that is make the bottom of each fraction equal.  In this case, (x+3)(x+5).  You must then multiply the numerator (the top part of the fraction) in each fraction by the new multiplier in the denominator.  You'll end up with:

[x(x+5)]/[(x+3)(x+5)] + [6(x+3)]/[(x+5)(x+3)]

distribute in the numerators and add to get:

[(x^2+5x) + (6x+18)]/[(x+3)(x+5)]

combine like terms in the numerator to get:

(x^2+11x+18)/[(x+3)(x+5)]

factor the numerator to get:

[(x+2)(x+9)]/[(x+3)(x+5)]