Here are the steps required for Adding and Subtracting Rational Expressions:
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1 Here are the steps required for Adding and Subtracting Rational Expressions: Step 1: Factor the denominator of each fraction to help find the LCD. Step 3: Find the new numerator for each fraction. To find the new numerators for each fraction compare the denominator of each of the original fractions to the LCD and write down everything different about the LCD in the numerator of that fraction. You should also consider using the letters LCD in the denominators instead of the actual LCD because this will make it less tempting to reduce the fractions. Step 4: Combine the fraction by adding or subtracting the numerators and keeping the LCD. When subtracting, notice that the subtraction sign is moved into the numerator so it can be distributed later if needed. Step 5: Simplify the numerator by distributing and combining like terms. Step 6: Factor the numerator if you can and replace the letters LCD with the actual LCD. Step 7: Simplify or reduce the rational expression if you can. Remember to reduce rational expressions the factors must be exactly the same in both the numerator and denominator. Step 1: Factor the denominator of each fraction to help find the LCD. Step 3: Find the new numerator for each fraction. If you compare the first fraction to the LCD the (x 3) is different, so it was written in the numerator. In the second fraction the (x + 2) was different. Step 4: Combine the fraction by adding or subtracting the numerators and keeping the LCD. Step 5: Simplify the numerator by distributing and combining like terms. Step 6: Factor the numerator if you can and replace the letters LCD with the actual LCD. Step 7: Simplify or reduce the rational expression if you can. In this case, the rational expression cannot be simplified.
2 Example 2 Simplify: Step 1: Factor the denominator of each fraction to help find the LCD. Step 3: Find the new numerator for each fraction. If you compare the first fraction to the LCD the (x 5) is different, so it was written in the numerator. In the second fraction the (x + 3) was different. Step 4: Combine the fraction by adding or subtracting the numerators and keeping the LCD. Step 5: Simplify the numerator by distributing and combining like terms. Step 6: Factor the numerator if you can and replace the letters LCD with the actual LCD. Step 7: Simplify or reduce the rational expression if you can. In this case, the rational expression cannot be simplified.
3 Here are the steps required for Multiplying Rational Expressions: Step 2: Cancel or reduce the fractions. Remember in the numerator with something in the the numerator and denominator the two factors Step 3: Rewrite the remaining factor. Notice that the numerator or denominator. Step 2: Cancel or reduce the fractions. Remember Step 3: Rewrite the remaining factor. Notice that Example 2 Simplify: Step 2: Cancel or reduce the fractions. Remember Step 3: Rewrite the remaining factor. Notice that
4 Here are the steps required for Dividing Rational Expressions: Step 2: Change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. Step 3: Cancel or reduce the fractions. Remember in the numerator with something in the the numerator and denominator the two factors Step 4: Rewrite the remaining factor. Notice that the numerator or denominator. Step 2: Change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. Step 3 : Cancel or reduce the fractions. Remember Step 4 : Rewrite the remaining factor. Notice that
5 Example 2 Simplify: Step 2: Change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. Step 3 : Cancel or reduce the fractions. Remember Step 4 : Rewrite the remaining factor. Notice that
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