Respuesta :
Step-by-step explanation:
multiplying/dividing rational expressions
The course of action of multiplying and dividing the Rational expressions is same as multiplying and dividing the numeric fractions.
To multiply
- First determine the greatest common factors of the numerator and denominator.
- Then, regrouping the factors to make fractions equal to one.
- Then, multiplying any remaining factors.
For example,
[tex]\frac{5}{14}a^2\:.\:\frac{7}{10a^3}[/tex]
Find if there are excluded values - values of a which can generate 0 as a denominator
[tex]10a^3\:=\:0[/tex]
[tex]a = 0[/tex]
The domain is all a ≠ 0
[tex]\mathrm{Multiply\:fractions}:\quad \:a\cdot \frac{b}{c}\cdot \frac{d}{e}=\frac{a\:\cdot \:b\:\cdot \:d}{c\:\cdot \:e}[/tex]
[tex]\frac{5\cdot \:7a^2}{14\cdot \:10a^3}[/tex]
[tex]\mathrm{Refine}[/tex]
[tex]\frac{35a^2}{140a^3}[/tex]
[tex]\mathrm{Cancel\:the\:common\:factor:}\:35[/tex]
[tex]\frac{a^2}{4a^3}[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=\frac{1}{x^{b-a}}[/tex]
As
[tex]\frac{a^2}{a^3}=\frac{1}{a^{3-2}}[/tex]
So,
[tex]\frac{1}{4a^{3-2}}[/tex]
[tex]\mathrm{Subtract\:the\:numbers:}\:3-2=1[/tex]
[tex]\frac{1}{4a}[/tex]
To Divide
- First rewriting the division as multiplication by the reciprocal of the denominator
- The remaining steps are then the same as for multiplication.
For example,
[tex]\frac{5x^2}{9}\:\div \frac{15x^3}{27}[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}[/tex]
[tex]\frac{5x^2}{9}\times \frac{27}{15x^3}[/tex]
x can not be zero i.e. x ≠ 0
[tex]\frac{5x^2}{9}\times \frac{9}{5x^3}[/tex]
[tex]\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}[/tex]
[tex]\frac{5x^2\times \:9}{9\times \:5x^3}[/tex]
[tex]\mathrm{Cancel\:the\:common\:factor:}\:5[/tex]
[tex]\frac{x^2\times \:9}{9x^3}[/tex]
[tex]\mathrm{Cancel\:the\:common\:factor:}\:9[/tex]
[tex]\frac{x^2}{x^3}[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=\frac{1}{x^{b-a}}[/tex]
[tex]\frac{x^2}{x^3}=\frac{1}{x^{3-2}}[/tex]
[tex]\frac{1}{x^{3-2}}[/tex]
[tex]\mathrm{Subtract\:the\:numbers:}\:3-2=1[/tex]
[tex]\frac{1}{x}[/tex]
Therefore, the main difference between multiplying/dividing rational expressions is during multiplying we
- First determine the greatest common factors of the numerator and denominator
and during dividing we
- First rewrite the division as multiplication by the reciprocal of the denominator
Adding/subtracting rational expressions
If the two rational expressions that we would like to want to add or subtract have the same denominator we just add/subtract the numerators which each other.
For example, when we add two rational expressions
[tex]\frac{x}{x-1}\:+\:\frac{3-x}{x-1}[/tex]
[tex]\mathrm{Apply\:rule}\:\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}[/tex]
[tex]\frac{x+3-x}{x-1}[/tex]
[tex]\frac{3}{x-1}[/tex]
And when we subtract two rational expressions
[tex]\frac{x}{x-1}\:-\:\frac{3-x}{x-1}[/tex]
[tex]\mathrm{Apply\:rule}\:\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}[/tex]
[tex]\frac{x-\left(-x+3\right)}{x-1}[/tex]
[tex]\frac{2x-3}{x-1}[/tex]
Keywords: ration expression, orations
Learn more about operations on algebraic expressions from brainly.com/question/12134889
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