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emeraldisles's avatar

How do you go about adding polynomials with fractions in parantheses?

Asked by emeraldisles (1949points) January 5th, 2012

The problem is( 1/16x^2+1/8)+(¼x^2–3/10x-½). The answer is supposed to be 5/16x^2–3/10x-3/8. All I can figure out is that the numbers/fractions all need to be changed into least common denominator. Have no idea how to get to the next step to get this answer?Help.

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4 Answers

Response moderated (Writing Standards)
Charles's avatar

No they don’t need to be to the LCD – that rule is for adding, not multiplying.

Your problem written in your post is very easy.

(A +B) (C+D+E) = AC+AD+AE+BC+BD+BE = 1/64X^2…

roundsquare's avatar

@Charles he IS doing adding.

Okay, lets do an easier one:

(⅓x + 2/5) + (¾x + ½)

Take the “x terms.” These are ⅓x and ¾x Lets get common denominators:
⅓x = 4/12x
¾x = 9/12x
4/12x + 9/12x = (4/12 + 9/12)x = 13/12x

Take the numbers. These are 2/5 and ½. Lets get common denominators:
2/5 = 4/10
½ = 5/10
2/5 + ½ = 4/10 + 5/10 = 9/10

So, the total is
13/12x + 9/10

————————————————————————————————————————————————————-

Okay, lets make it a bit harder.
(1/5x^2 + ⅓x + 2/5) + (⅔x^2 + ¾x + ½)

Take the “x^2 terms.” These are 1/5x^2 and ⅔x^2 Lets get common denominators:
1/5x^2 = 3/15x^2
⅔x^2 = 10/15x^2
3/15x^2 + 10/15x^2 = (3/15 + 10/15)x^2 = 13/15x^2

Take the “x terms.” These are ⅓x and ¾x Lets get common denominators:
⅓x = 4/12x
¾x = 9/12x
4/12x + 9/12x = (4/12 + 9/12)x = 13/12x

Take the numbers. These are 2/5 and ½. Lets get common denominators:
2/5 = 4/10
½ = 5/10
4/10 + 5/10 = 9/10

So, the total is
13/15x^2 + 13/12x + 9/10

———————————————————————————————————————-

Hope this helps. If you want more explanation, please ask.

s321scba's avatar

disregard the parenthesies, and only add like terms, coefficients with the same variables, don’t add 3a to 4b or 5a^2 to 6a, order of operations

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