Subtract: x² – 2x + 1 x² – 1 We will factor each denominator, find the LCD, and build the rational expressions so each one has the LCD as its denominator. Since the denominators are different, we cannot subtract these rational expressions in their present form. We factor each denominator to find the LCD: x² – 2x + 1 = (x – 1)(x – 1) = (x – 1)2 x² – 1 = (x + 1)(x – 1) The greatest number of times x - 1 appears is twice. The greatest number of times x + 1 appears is once. The LCD is (x – 1)²(x + 1) or (x – 1)(x – 1)(x + 1). We now write each rational expression with its denominator in factored form. Then we multiply each numerator and denominator by the missing factor, so that each rational expression has a denominator of (x - 1)(x – 1)(x + 1). x + 1 x + 1 (x – 1)(x – 1) X - 4 (x + 1)(x – 1) x + 1 + 1 Write each denominator in factored form. x² – 2x + 1 1. x + 1 (x -– 1)(x – 1) x² + 2x + 1 (x – 1)(x – 1)(x + 1) (x² + 2x + 1) - (x² – 5x + 4) (x – 1)(x – 1)(x + 1) X - 4 Build each rational expression. (x + 1)(x – 1) X - 1 x2 - 5x + 4 (x + 1)(x – 1)(x – 1) Multiply the numerators using the FOIL method. Multiply the denominators. Subtract the numerators. Write the difference over the common denominator. x² + 2x + 1 – x² + 5x – 4 (x – 1)(x – 1)(x + 1) In the numerator, subtract the polynomials. %3D Combine like terms. The result does not simplify. (x – 1)(x – 1)(x + 1) a + 2 a2 - 4a + 4 a - Subtract:
Subtract: x² – 2x + 1 x² – 1 We will factor each denominator, find the LCD, and build the rational expressions so each one has the LCD as its denominator. Since the denominators are different, we cannot subtract these rational expressions in their present form. We factor each denominator to find the LCD: x² – 2x + 1 = (x – 1)(x – 1) = (x – 1)2 x² – 1 = (x + 1)(x – 1) The greatest number of times x - 1 appears is twice. The greatest number of times x + 1 appears is once. The LCD is (x – 1)²(x + 1) or (x – 1)(x – 1)(x + 1). We now write each rational expression with its denominator in factored form. Then we multiply each numerator and denominator by the missing factor, so that each rational expression has a denominator of (x - 1)(x – 1)(x + 1). x + 1 x + 1 (x – 1)(x – 1) X - 4 (x + 1)(x – 1) x + 1 + 1 Write each denominator in factored form. x² – 2x + 1 1. x + 1 (x -– 1)(x – 1) x² + 2x + 1 (x – 1)(x – 1)(x + 1) (x² + 2x + 1) - (x² – 5x + 4) (x – 1)(x – 1)(x + 1) X - 4 Build each rational expression. (x + 1)(x – 1) X - 1 x2 - 5x + 4 (x + 1)(x – 1)(x – 1) Multiply the numerators using the FOIL method. Multiply the denominators. Subtract the numerators. Write the difference over the common denominator. x² + 2x + 1 – x² + 5x – 4 (x – 1)(x – 1)(x + 1) In the numerator, subtract the polynomials. %3D Combine like terms. The result does not simplify. (x – 1)(x – 1)(x + 1) a + 2 a2 - 4a + 4 a - Subtract:
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter3: Polynomial And Rational Functions
Section3.4: Real Zeros Of Polynomials
Problem 1E: If the polynomial function Px=anxn+an-1xn-1++a1x+a0 has integer coefficients, then the only numbers...
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Question
Transcribed Image Text:x + 1
x2 - 2x + 1
х — 4
Subtract:
x2
- 1
We will factor each denominator, find the LCD, and build the rational expressions so each one has the LCD as its denominator.
Since the denominators are different, we cannot subtract these rational expressions in their present form.
We factor each denominator to find the LCD:
x2 - 2x + 1 = (x – 1)(x – 1) = (x – 1)2
x2 - 1 = (x + 1)(x – 1)
The greatest number of times x –
1 appears is twice.
The greatest number of times x + 1 appears is once.
The LCD is (x – 1)2(x + 1) or (x – 1)(x – 1)(x + 1).
We now write each rational expression with its denominator in factored form. Then we multiply each numerator and denominator by the missing factor, so that each rational
expression has a denominator of (x – 1)(x – 1)(x + 1).
х+ 1
х — 4
x + 1
х — 4
Write each denominator in factored form.
-
-
x2 - 2x + 1
1
(х — 1)(х — 1)
(x + 1)(x – 1)
x + 1
x + 1
X + 1
X - 4
X - 1
Build each rational expression.
-
(х — 1)(х — 1)
(x + 1)(x – 1)
х — 1
x2 - 5x + 4
x2 + 2x + 1
(x – 1)(x – 1)(x + 1)
(x² + 2x + 1) – (x² – 5x + 4)
(x – 1)(x – 1)(x + 1)
x2 + 2x + 1 – x² + 5x
(x – 1)(x – 1)(x + 1)
Multiply the numerators using the FOIL method.
Multiply the denominators.
(x + 1)(x – 1)(x – 1)
Subtract the numerators. Write the difference over the common denominator.
- 4
In the numerator, subtract the polynomials.
Combine like terms. The result does not simplify.
(x – 1)(x – 1)(x + 1)
a + 2
a - 1
Subtract:
a2 - 4a + 4
a2 - 4
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