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Question
Math
Posted 9 months ago

Write the following as a single rational expression.
170+50xx÷120+30xx
\frac{170+50 x}{x} \div \frac{120+30 x}{x}
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Answer from Sia
Posted 9 months ago
Solution by Steps
step 1
The given expression is 170+50xx÷120+30xx\frac{170 + 50x}{x} \div \frac{120 + 30x}{x}
step 2
To divide by a fraction, we multiply by its reciprocal: 170+50xx×x120+30x\frac{170 + 50x}{x} \times \frac{x}{120 + 30x}
step 3
Simplify the expression: (170+50x)⋅xx⋅(120+30x)\frac{(170 + 50x) \cdot x}{x \cdot (120 + 30x)}
step 4
Cancel out the xx terms: 170+50x120+30x\frac{170 + 50x}{120 + 30x}
step 5
Factor out common terms: 50x+17030x+120=50(x+175)30(x+4)\frac{50x + 170}{30x + 120} = \frac{50(x + \frac{17}{5})}{30(x + 4)}
step 6
Simplify the fraction: 5(x+175)3(x+4)=5x+173x+12\frac{5(x + \frac{17}{5})}{3(x + 4)} = \frac{5x + 17}{3x + 12}
Answer
5x+173x+12\frac{5x + 17}{3x + 12}
Key Concept
Simplifying Rational Expressions
Explanation
To simplify a rational expression involving division, multiply by the reciprocal and then simplify by canceling common terms.

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