Question

using appropriate properties of addition, find the following (

$(i) \: \frac{4}{5} + \frac{11}{7} + \frac{ - 7}{5} + \ \: \ \frac{ - 2}{7}$
$(i) \: \frac{3}{7} + \frac{4}{9} + \frac{ - 5}{21} + \frac{2}{3}$
PLEASE ANSWER

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Answer 1

Answer:

The quotient of two polynomial expressions is called a rational expression. We can apply the properties of fractions to rational expressions, such as simplifying the expressions by canceling common factors from the numerator and the denominator. To do this, we first need to factor both the numerator and denominator. Let’s start with the rational expression shown.

Step-by-step explanation:

\displaystyle \frac{{x}^{2}+8x+16}{{x}^{2}+11x+28}

x

2

+11x+28

x

2

+8x+16

We can factor the numerator and denominator to rewrite the common factor

Then we can simplify that expression by canceling the common factor \displaystyle \left(x+4\right)(x+4).

\displaystyle \frac{x+4}{x+7}

x+7

x+4

Answer 2

$1) \: answer$

$\frac{4}{5} + \frac{11}{7} + \frac{ - 7}{5} + \frac{ - 2}{7}$

$= \frac{4}{5} + \frac{ - 7}{5} + \frac{11}{7} + \frac{ - 2}{7}$

$= \frac{(4 - 7)}{5} + \frac{(11 - 2)}{7}$

$= \frac{3}{5} + \frac{9}{7}$

$= \frac{3 \times 7}{5 \times 7} + \frac{9 \times 5}{7 \times 5}$

$= \frac{21}{35} + \frac{45}{35}$

$= \frac{21 + 45}{35}$

$= \frac{66}{35}$

$2) \: answer$

$= \frac{3}{7} + \frac{4}{9} + \frac{ - 5}{21} + \frac{2}{3}$

$= \frac{3 \times 3}{7 \times 3} + \frac{ - 5}{21} + \frac{2 \times 3}{3 \times 3} + \frac{4}{9}$

$= \frac{9}{21} + \frac{ - 5}{21} + \frac{6}{9} + \frac{4}{9}$

$= \frac{9 - 5}{21} + \frac{6 + 4}{9}$

$= \frac{4}{21} + \frac{10}{9}$

$= \frac{4 \times 9}{21 \times 9} + \frac{10 \times 21}{9 \times 21}$

$= \frac{36}{189} + \frac{210}{189}$

$= \frac{36 + 210}{189}$

$= \frac{246}{189}$

$= \frac{82}{63}$