
Rational Expression of Polynomials


1.
Reduced Terms 



2.
Addition, Subtraction, Multiplication, Division 



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Rational Expression of Polynomials

1. Find Reduced Term of `(4X^225)/(8X^3125)`
` = ((4X^2  25))/((8X^3  125))`
` = ((2X5)(2X+5))/((2X5)(4X^2+10X+25))`
`"Now cancel the common factor " (2X  5)`
` = ((2X+5))/((4X^2+10X+25))`
2. Find `(X^2X+1)/(2(X1))  (X^2+X+1)/(2(X+1))  (4X)/((X^21)^2)`
` = ((X^2  X + 1))/(2(X  1))  ((X^2 + X + 1))/(2(X + 1))  (4X)/((X^2  1)^2)`
` = ((X^2X+1))/(2(X1))  ((X^2+X+1))/(2(X+1))  (4X)/((X1)^2(X+1)^2)`
` = ((X^2  X + 1) × (X  1)(X + 1)^2  (X^2 + X + 1) × (X  1)^2(X + 1)  4X × 2)/(2(X1)^2(X+1)^2)`
` = ((X^5  X^3 + X^2  1)  (X^5  X^3  X^2 + 1)  8X)/(2(X1)^2(X+1)^2)`
` = ((2X^228X))/(2(X1)^2(X+1)^2)`

Rational Expression of Polynomials

Here X^{2} = X^2 = X2 and 2X = 2*X
1. Find Reduced Terms of Rational Expressions
(1) `(X^2+2X+1)/(2(X+1))`
(2) `(2(X^2Y^2))/(3(X^3Y^3))`
(3) `(X^41)/(X^2+1)`
(4) `(X^29)/(X^327)`
2. Find addition, Subtraction, multiplication, division of two and three terms of rational polynomials.
(1) `(X3)/(X+1)  (X6)/(X)`
(2) `(4x+1)/(4x1)  (4x1)/(4x+1)  3`
(3) `(1)/(6X^213X+6) + (1)/(8X^214X+3)  (1)/(12X^211X+2)`
(4) `(X+2)/(X^24X+3) xx (X+3)/(X^23X+2)  (X+1)/(X^25X+6)`
(5) `(X^31)/(X1) + (X^3+1)/(X+1)  (2(X^41))/(X^21)`



