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FromTheMoon [43]
3 years ago
14

Help me to answer now ineed this Please...

Mathematics
1 answer:
Vera_Pavlovna [14]3 years ago
5 0
ANSWER TO QUESTION 1

\frac{\frac{y^2-4}{x^2-9}} {\frac{y-2}{x+3}}

Let us change middle bar to division sign.

\frac{y^2-4}{x^2-9}\div \frac{y-2}{x+3}

We now multiply with the reciprocal of the second fraction

\frac{y^2-4}{x^2-9}\times \frac{x+3}{y-2}

We factor the first fraction using difference of two squares.

\frac{(y-2)(y+2)}{(x-3)(x+3)}\times \frac{x+3}{y-2}

We cancel common factors.

\frac{(y+2)}{(x-3)}\times \frac{1}{1}

This simplifies to

\frac{(y+2)}{(x-3)}

ANSWER TO QUESTION 2

\frac{1+\frac{1}{x}} {\frac{2}{x+3}-\frac{1}{x+2}}

We change the middle bar to the division sign

(1+\frac{1}{x}) \div (\frac{2}{x+3}-\frac{1}{x+2})

We collect LCM to obtain

(\frac{x+1}{x})\div \frac{2(x+2)-1(x+3)}{(x+3)(x+2)}

We expand and simplify to obtain,

(\frac{x+1}{x})\div \frac{2x+4-x-3}{(x+3)(x+2)}

(\frac{x+1}{x})\div \frac{x+1}{(x+3)(x+2)}

We now multiply with the reciprocal,

(\frac{(x+1)}{x})\times \frac{(x+2)(x+3)}{(x+1)}

We cancel out common factors to  obtain;

(\frac{1}{x})\times \frac{(x+2)(x+3)}{1}

This simplifies to;

\frac{(x+2)(x+3)}{x}

ANSWER TO QUESTION 3

\frac{\frac{a-b}{a+b}} {\frac{a+b}{a-b}}

We rewrite the above expression to obtain;

\frac{a-b}{a+b}\div {\frac{a+b}{a-b}}

We now multiply by the reciprocal,

\frac{a-b}{a+b}\times {\frac{a-b}{a+b}}

We multiply out to get,

\frac{(a-b)^2}{(a+b)^2}

ANSWER T0 QUESTION 4

To solve the equation,

\frac{m}{m+1} +\frac{5}{m-1} =1

We multiply through by the LCM of (m+1)(m-1)

(m+1)(m-1) \times \frac{m}{m+1} + (m+1)(m-1) \times \frac{5}{m-1} =(m+1)(m-1) \times 1

This gives us,

(m-1) \times m + (m+1) \times 5}=(m+1)(m-1)

m^2-m+ 5m+5=m^2-1

This simplifies to;

4m-5=-1

4m=-1-5

4m=-6

\Rightarrow m=-\frac{6}{4}

\Rightarrow m=-\frac{3}{2}

ANSWER TO QUESTION 5

\frac{3}{5x}+ \frac{7}{2x}=1

We multiply through with the LCM  of 10x

10x \times \frac{3}{5x}+10x \times \frac{7}{2x}=10x \times1

We simplify to get,

2 \times 3+5 \times 7=10x

6+35=10x

41=10x

x=\frac{41}{10}

x=4\frac{1}{10}

Method 1: Simplifying the expression as it is.

\frac{\frac{3}{4}+\frac{1}{5}}{\frac{5}{8}+\frac{3}{10}}

We find the LCM of the fractions in the numerator and those in the denominator separately.

\frac{\frac{5\times 3+ 4\times 1}{20}}{\frac{(5\times 5+3\times 4)}{40}}

We simplify further to get,

\frac{\frac{15+ 4}{20}}{\frac{25+12}{40}}

\frac{\frac{19}{20}}{\frac{37}{40}}

With this method numerator divides(cancels) numerator and denominator divides (cancels) denominator

\frac{\frac{19}{1}}{\frac{37}{2}}

Also, a denominator in the denominator multiplies a numerator in the numerator of the original fraction while a numerator in the denominator multiplies a denominator in the numerator of the original fraction.

That is;

\frac{19\times 2}{1\times 37}

This simplifies to

\frac{38}{37}

Method 2: Changing the middle bar to a normal division sign.

(\frac{3}{4}+\frac{1}{5})\div (\frac{5}{8}+\frac{3}{10})

We find the LCM of the fractions in the numerator and those in the denominator separately.

(\frac{5\times 3+ 4\times 1}{20})\div (\frac{(5\times 5+3\times 4)}{40})

We simplify further to get,

(\frac{15+ 4}{20})\div (\frac{(25+12)}{40})

\frac{19}{20}\div \frac{(37)}{40}

We now multiply by the reciprocal,

\frac{19}{20}\times \frac{40}{37}

\frac{19}{1}\times \frac{2}{37}

\frac{38}{37}
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