Adding, subtracting, multiplying, dividing of rational expressions polynomials Examples

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Home > Algebra calculators > Adding, subtracting, multiplying, dividing of rational expressions polynomials example

Adding, subtracting, multiplying, dividing of rational expressions polynomials example ( Enter your problem )

( Enter your problem )

Examples

Other related methods

Reduce rational expressions
Adding, subtracting, multiplying, dividing of rational expressions polynomials

1. Reduce rational expressions
(Previous method)

1. Examples

1. Find $(1)/(x+1) + (x)/(x-1)$

Solution:

$=1/(x+1)+x/(x-1)$

$=(1 xx (x-1)+x xx (x+1))/((x+1)(x-1))$

$=((x-1)+(x^2+x))/((x+1)(x-1))$

$=(2x-1+x^2)/((x+1)(x-1))$

2. Find $(1)/(x+1) - (x)/(x-1)$

Solution:

$=1/(x+1)-x/(x-1)$

$=(1 xx (x-1)-x xx (x+1))/((x+1)(x-1))$

$=((x-1)-(x^2+x))/((x+1)(x-1))$

$=(-1-x^2)/((x+1)(x-1))$

3. Find $(x-1)/(x+1) * (x)/(x-1)$

Solution:

$=(x-1)/(x+1)×x/(x-1)$

$=x/(x+1)$

4. Find $(1)/(x-1) / (x)/(x-1)$

Solution:

$=1/(x-1)/(x/(x-1))$

$=1/(x-1)×(x-1)/x$

$=1/x$

5. Find $(1)/(x-1) + (x)/(x-1) - (1)/(x+1)$

Solution:

$=1/(x-1)+x/(x-1)-1/(x+1)$

$=(1 xx (x+1)+x xx (x+1)-1 xx (x-1))/((x-1)(x+1))$

$=((x+1)+(x^2+x)-(x-1))/((x-1)(x+1))$

$=(x+2+x^2)/((x-1)(x+1))$

6. Find $(1)/(x-1) / (x)/(x-1) * (1)/(x+1)$

Solution:

$=1/(x-1)/(x/(x-1))×1/(x+1)$

$=1/(x-1)×(x-1)/x×1/(x+1)$

$=1/(x^2+x)$

7. Find $(x-1)/(x+1) - (x+1)/(x-1) + (4x)/(x^2-1)$

Solution:

$=(x-1)/(x+1)-(x+1)/(x-1)+(4x)/(x^2-1)$

$=(x-1)/(x+1)-(x+1)/(x-1)+(4x)/((x-1)(x+1))$

$=((x-1) xx (x-1)-(x+1) xx (x+1)+4x)/((x+1)(x-1))$

$=((x^2-2x+1)-(x^2+2x+1)+4x)/((x+1)(x-1))$

$=0/((x+1)(x-1))$

$=0$

8. Find $(x+2)/(x^2-4x+3) - (x+3)/(x^2-3x+2) + (x+1)/(x^2-5x+6)$

Solution:

$=(x+2)/(x^2-4x+3)-(x+3)/(x^2-3x+2)+(x+1)/(x^2-5x+6)$

$=(x+2)/((x-1)(x-3))-(x+3)/((x-1)(x-2))+(x+1)/((x-2)(x-3))$

$=((x+2) xx (x-2)-(x+3) xx (x-3)+(x+1) xx (x-1))/((x-3)(x-2)(x-1))$

$=((x^2-4)-(x^2-9)+(x^2-1))/((x-3)(x-2)(x-1))$

$=(4+x^2)/((x-3)(x-2)(x-1))$

9. Find $(x^2+5x+4)/(x^2-4) * (x^2-5x+6)/(x^2-16) / (x^2-2x-3)/(x^2-2x-8)$

Solution:

$=(x^2+5x+4)/(x^2-4)×(x^2-5x+6)/(x^2-16)/((x^2-2x-3)/(x^2-2x-8))$

$=((x+1)(x+4))/((x-2)(x+2))×((x-2)(x-3))/((x-4)(x+4))/(((x+1)(x-3))/((x+2)(x-4)))$

$=((x+1)(x+4))/((x-2)(x+2))×((x-2)(x-3))/((x-4)(x+4))×((x+2)(x-4))/((x+1)(x-3))$

$=1$

This material is intended as a summary. Use your textbook for detail explanation.
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