University:
Campbell University
Course:
MATH 111 | College Algebra
Academic year:

2022
Views:

52

Pages:

2
Author:

accionox1v

Complex Fractions There are two types of complex fractions… Type I: There is only one fraction in the top and the bottom. Example: 3 4 _____ 7 8 or x 1 x2 _______ x4 2x  4 To simplify, just rewrite the problem as a division problem: 3 7  4 8 or x 1 x  4  x  2 2x  4 Now, we know how to divide fractions (invert and multiply). . . . . . 3 8  4 7 or x  1 2x  4  x2 x4 Factor and Reduce: 3 8  4 7 x  1 2( x  2)  x2 x4 3 2  1 7 x 1 2  1 x4 6 7 2( x  1) x4 Don’t panic because they look scary. They are nothing but a division problem. On to Type II …….. Type 2: Has more than one fraction in the top and bottom. Example: 1 x 1 1  2 x 2 Steps to simplify: 1. Turn everything into a fraction by using 1 as a denominator: 2. Examine all the fractions and find the LCD. 2 1  1 x 1 1  2 x LCD = 2x 3. Put each fraction into ( ) and multiply by the LCD: 2x  2   1  2x    1 1  x 1 2x  1   1  2x    1  2  x 1 4. Reduce and multiply. (Can you see what this step accomplishes?) 2x  2   1  2x    1 1  x 1 2x  1   1  2x    1  2  x 1 5. Combine like terms if possible. 4x  2 x2 6. This is the last step. Factor and reduce if possible: 2(2 x  1) x2 Since we are unable to reduce, we are done!