Q. Simplify. Express your answer as a single fraction in simplest form. 47wx5−7x34
Identify Common Denominator: Identify the common denominator for the two fractions.Since the fractions have different denominators, we need to find a common denominator to combine them. The first fraction has a denominator of 4, and the second fraction has a denominator of 7x3. The least common denominator (LCD) will be the product of these two denominators, which is 4×7x3=28x3.
Rewrite with Common Denominator: Rewrite each fraction with the common denominator.We will multiply the numerator and denominator of each fraction by whatever is necessary to get the denominator to be the LCD.For the first fraction, 47wx5, we need to multiply the numerator and denominator by 7x3 to get the common denominator of 28x3.(47wx5)⋅(7x37x3)=28x349wx8For the second fraction, 7x34, we need to multiply the numerator and denominator by 4 to get the common denominator of 28x3.(7x34)⋅(44)=28x316
Combine Fractions: Combine the fractions.Now that both fractions have the same denominator, we can combine them by subtracting the numerators.(28x349wx8)−(28x316)=28x349wx8−16
Simplify Expression: Simplify the expression if possible.In this case, there are no common factors between the numerator and the denominator that can be canceled out, so the expression is already in its simplest form.(49wx8−16)/28x3 is the simplified expression.
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