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12.6A Adding Rational Expressions with SAME denominators
Review: a. = 5 7
Review: b. =
Find a common denominator Multiply top and bottom Add top only, keep bottom Factor if possible Simplify
a. = 1 4 = 12 3x 4 x
b. = 10. x 2 + 1
c. = y + 3 y
d. = 2x + 1 x – 2
Find a common denominator Multiply top and bottom Make Adding (distribute negative) Factor if possible Simplify
Example 2: find the difference.
a. = 2. z2z2
b. = -5n + 4 n + 2
c. = 2x – 5 x – 1
d. = 2x + 4 x + 2 2 x+ 2 = 2(x + 2) x + 2 = 2
e. = x2x2 – 8x+7 x – 7 x x -7 = (x-7)(x-1) x – 7 = x-1
Example 3: Find the sum or difference. Then simplify completely.
a. = 3x + 9 x + 3 3 x+ 3 3(x + 3) x + 3 = 3
b. = -2m + 16 (m+7)(m-8) -2 m– 8 = -2(m-8) (m+7)(m-8) = -2 m+7
c. 4x 2 – 2x– 2 x(x-1) = 2x x +1 = 2(2x+1)(x-1) x(x-1) = 2(2x+1) x 2 2x 2 – x– 1
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