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3 years ago

Add and simplify 3/14+9/14

2 answers:

8 0

This is relatively simple because both have the same common denominator. All you must do is add 3 and 9 together. That gives you 12/14. To simplify we can half both numbers down to 6/7.
Hope that helps !
<3

Olegator [25]3 years ago

5 0

Since both of the denominators are the same number, you would leave that alone. Then, add both of the numerators together, which is 12. The answer is 12/14. To simplify, divide both sides by a number that goes into both of them. The answer is 6/7. Hope this helped!

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For each rational expression, identify the greatest common factor, write the expression in factored form, and simplify.

podryga [215]

Answer:

1) $9a,\frac{3^{3n}}{5^{n^{5}}},\frac{x+x^{3}}{x^{3}},\frac{a}{a^{5}-1},\frac{3b+1}{5b^{3}}, \frac{3y}{y^{2}-2},\frac{2x^{2}+4x-1}{3}, \frac{(p^{4}-5q^{2})}{(2p^{2}q^{3}+6p^{4}q^{2})}$ 2) $\frac{xy^{4}+7x^{5}y^{2}+49}{2x^{5}y^{2}}$

Prime factorize the parameters 7,49,28,343 pick its GCF=7. As for the variables choose the ones raised to the least exponent and divide each term by this.

Then, after that part. All that's left is a simplification dividing the members by the common monomial.

Step-by-step explanation:

1) Let's proceed this way. For the numbers, to find the GCF is simply to Prime factor the numbers and pick greatest common factor. When it comes to variables the point is to choose the variable with the least exponent.

$\frac{27a^{4}}{3a^{3}}\: GCF=3a^{3}\Rightarrow \frac{27a^{4}:3a^3}{3a^{3}:3a^{3}}=9a\\\\\frac{15m^{5n}}{25m^{2n^{6}}}\:GCF=5 \Rightarrow \frac{15m^{5n}:5m^{2n}}{25m^{2n^{6}}:5m^{2n}}=\frac{3^{3n}}{5^{n^{5}}}\\\\\frac{x^{4}+x^{6}}{x^{3}}\:GCF=x^3\Rightarrow \frac{x^{4}:x^{3}+x^{6}:x^{3}}{x^{3}:x^{3}}\Rightarrow \frac{x+x^{3}}{x^{3}}$

$\frac{a^{5}}{a^{9}-a^{4}}\:GCF:a^{4}\Rightarrow \frac{a^{5}:a^{4}}{a^{9}:a^{4}-a^{4}:a^{4}}\Rightarrow \frac{a}{a^{5}-1}\:or\:\frac{a^{4}(a)}{a^{4}(a^{5}-1)}=\frac{a}{a^{5}-1}\\\frac{3b^{2}+b}{5b^{4}}\:GCF=b\Rightarrow \frac{b(3b+1)}{b(5b^{3})}=\frac{3b+1}{5b^{3}}\\\frac{21y^{3}}{7y^4-14y^2}\:GCF=7y^{2}\Rightarrow \frac{7y^{2}(3y)}{7y^{2}(y^{2}-2)}\Rightarrow \frac{3y}{y^{2}-2}$

$\frac{6x^{4}+12x^{3}-3x^{2}}{9x^{2}}\:GCF=3x^{2}\Rightarrow \frac{3x^{2}(2x^{2}+4x-1)}{3x^{2}(3)}\Rightarrow \frac{2x^{2}+4x-1}{3}$

$\frac{2p^{5}q-10pq^{3}}{4p^{3}q^{4}+12p^{5}q^{3}}\:GCF=2pq \Rightarrow \frac{2pq(p^{4}-5q^{2})}{2pq(2p^{2}q^{3}+6p^{4}q^{2})}=\frac{(p^{4}-5q^{2})}{(2p^{2}q^{3}+6p^{4}q^{2})}$

2,3) <em>Write your own example of a rational expression and demonstrate how to simplify the expression using GCF (greatest common factor).</em>

Write a rational expression with a gfc that has both a numeric part and a variable part.

Identify gfc and show how to simplify using gfc.

Well, similarly, to the previous ones. Prime factorize the parameters 7,49,28,343 pick its GCF=7. As for the variables choose the ones raised to the least exponent and divide each term by this.

Then, after that part. All that's left is a simplification dividing the members by the common term as it follows:

$\frac{7x^{2}y^{6}+49x^{6}y^{4}+343xy^{2}}{28x^{6}y^{4}}\Rightarrow GCF=7xy^{2}\Rightarrow \frac{7xy^{2}(xy^{4}+7x^{5}y^{2}+49)}{7xy^{2}(2x^{5}y^{2})}\Rightarrow \frac{xy^{4}+7x^{5}y^{2}+49}{2x^{5}y^{2}}$

3 0

3 years ago

If i have a job and get paid $8.50 an hour. If i work 5 hours everyday for two weeks, how much would I have?

ZanzabumX [31]

You would make approximate $42.50 each day. In two weeks you would make $595

8 0

3 years ago

Read 2 more answers

Jean adds 35 and 9. how can she solve using only equations to model her thinking?

Alexxandr [17]

She can break up the nine in to 3 three time and add it to 35

8 0

4 years ago

Read 2 more answers

Please help ! I need the answers to these ASAP

liq [111]

Answer:

16. 33° and 57°

17. 10x+20= mEBC

18. 92°

3 0

3 years ago

Answer each of the questions for the following diagram:

elena-s [515]

Answer:

vertical angles, x=5 The angles each measure 35 degrees

Step-by-step explanation:

These are vertical angles, so they are equal

3x+20 = 10x-15

Subtract 3x from each side

3x+20-3x = 10x-13-3x

20 = 7x-15

Add 15 to each side

20+15 = 3x-15+15

35=7x

Divide by 7

35/7 = 7x/7

5 =x

The angles are equal so they each measure

3x+20 = 3(5)+20 = 15+20 = 35

The each measure 35

7 0

4 years ago