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Home » Write the left-hand side as a single rational expression: - Aurero

Write the left-hand side as a single rational expression: - Aurero

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 A biotech patent includes 50 claims. One-fifth are independent. Of those, 30% contain novel gene edits. Of those, 60% are approved. How many are approved?

📌 Independent: 50 × 1/5 = <<50 / 5 = 10>>10.

📌 With novel edits: 10 × 0.3 = <<10 * 0.3 = 3>>3.

📌 Approved: 3 × 0.6 = <<3 * 0.6 = 1.8>> — no.

📌 × 0.6 = 1.8 — again.

📌 × 3/5 = 9/5 = 1.8.

📌 To get integer, use 50 × 0.3 = 15, 15 × 0.6 = 9 — yes.

📌 So: one-fifth of 50 is 10? 50/5=10, but 30% of 10=3, 60% of 3=1.8 — not good.

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rac{1}{2} \left[ \left( rac{1}{1} - rac{1}{3}
ight) + \left( rac{1}{2} - rac{1}{4}
ight) + \left( rac{1}{3} - rac{1}{5}
ight) + \cdots + \left( rac{1}{50} - rac{1}{52}
Most terms cancel. The positive terms that do not cancel are $ rac{1}...
The negative terms that do not cancel are $ -rac{1}{51}, -rac{1}{52}...
So the sum becomes:
rac{1}{2} \left( 1 + rac{1}{2} - rac
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