Q. Simplify. Express your answer as a single fraction in simplest form. 29b−bc5
Identify LCD: Identify the least common denominator (LCD) for the fractions.The fractions are 29b and bc5. The LCD for these fractions is 2bc because it is the smallest number that both denominators (2 and bc) will divide into without a remainder.
Rewrite fractions: Rewrite each fraction with the common denominator.To rewrite 29b with the common denominator, multiply both the numerator and the denominator by c to get (2⋅c)(9b⋅c). To rewrite bc5 with the common denominator, multiply both the numerator and the denominator by 2 to get (bc⋅2)(5⋅2).
Perform multiplication: Perform the multiplication from Step 2.For the first fraction, (9b×c)/(2×c) simplifies to 9bc/2bc. For the second fraction, (5×2)/(bc×2) simplifies to 10/2bc.
Combine fractions: Combine the fractions over the common denominator.Now that both fractions have the common denominator of 2bc, we can combine them into a single fraction:2bc9bc−2bc10=2bc9bc−10
Simplify numerator: Simplify the numerator if possible.In this case, the numerator 9bc−10 cannot be simplified further because there are no common factors between 9bc and 10.
Check for simplification: Check if the fraction can be simplified further.The fraction (9bc−10)/2bc is already in simplest form because the numerator and the denominator have no common factors other than 1.
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