Đáp án:
`a,`
`A = 7/35 × 10/9 + 7/19 × 9/35 - 2/35`
`⇔ A = 7/35 × 10/9 + 7/35 × 9/19 - 2/35`
`⇔ A = 7/35 × (10/9 + 9/19) - 2/35`
`⇔ A = 7/35 × 271/171 - 2/35`
`⇔ A = 271/855 - 2/35`
`⇔ A = 311/1197`
Vậy `A = 311/1197`
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$b,$
`B = (5 × 4^{15} × 9^9 - 4 × 3^{20} × 8^9)/(5 × 2^{10} × 6^{19} - 7 × 2^{29} × 27^6)`
`⇔ B = (5 × (2^2)^{15} × (3^2)^9 - 2^2 × 3^{20} × (2^3)^9)/(5 × 2^{10} × 2^{19} × 3^{19} - 7 × 2^{29} × (3^3)^6)`
`⇔ B = (5 × 2^{30} × 3^{18} - 3^{20} × 2^{29})/(5 × 2^{29} × 3^{19} - 7 × 2^{29} × 3^{18})`
`⇔ B = (5 × 2^{29} × 2 × 3^{18} - 3^2 × 3^{18} × 2^{29})/(5 × 2^{29} × 3^{18}×3 - 7 × 2^{29} × 3^{18})`
`⇔ B = (2^{29} × 3^{18} × (5 × 2 - 3^2) )/(2^{29} × 3^{18} × (5×3-7) )`
`⇔ B = (5 × 2 - 9)/(5 × 3 - 7)`
`⇔ B = (10 - 9)/(15 - 7)`
`⇔ B = 1/8`
Vậy `B = 1/8`
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$c,$
`C = (1 + 1/(1×3) ) (1 + 1/(2×4) ) (1 + 1/(3×5) ) (1 + 1/(4×6) ) ... (1 + 1/(98×100) )`
`⇔ C = ( (1×3)/(1×3) + 1/(1×3) ) ( (2×4)/(2×4) + 1/(2×4) ) ( (3×5)/(3×5) + 1/(3×5) ) ( (4×6)/(4×6) + 1/(4×6) ) ... ( (98×100)/(98×100) + 1/(98×100) )`
`⇔ C = (3/(1×3) + 1/(1×3) ) (8/(2×4) + 1/(2×4) ) (15/(3×5) + 1/(3×5) ) (24/(4×6) + 1/(4×6) ) ... ( 9800/(98×100) + 1/(98 × 100) )`
`⇔ C = 4/(1×3) × 9/(2×4) × 16/(3×5) × 25/(4×6) ... 9801/(98×100)`
`⇔ C = (2×2)/(1×3) × (3×3)/(2×4) × (4×4)/(3×5) × (5×5)/(4×6) ... (99×99)/(98×100)`
`⇔ C = (2×2×3×3×4×4×5×5...99×99)/(1×3×2×4×3×5×4×6...98×100)`
`⇔ C = (2×3×4...98×99)/(1×2×3×4...97×98) × (2×3×4...98×99)/(3×4×5...99×100)`
`⇔ C = 99 × 2/100`
`⇔ C = 99/50`
Vậy `C = 99/50`
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$d,$
`D = (155 - 10/7 - 5/11 + 5/23)/(403 - 26/7 - 13/11 + 13/23) + (3/5 + 3/13 - 0,9)/(7/91 + 0,2 - 3/10)`
`⇔ D = (5 × 31 - 5×2/7 - 5×1/11 + 5 × 1/23)/(13 × 31 - 13 × 2/7 - 13× 1/11 + 13 × 1/23) + (3/5 + 3/13 - 9/10)/(1/13 + 1/5 - 3/10)`
`⇔ D = (5 × (31 - 2/7 - 1/11 + 1/23) )/(13 × (31 - 2/7 - 1/11 + 1/23) ) + (3 × (1/5 + 1/13 - 3/10) )/(1/5 + 1/13 - 3/10)`
`⇔ D = 5/13 + 3`
`⇔ D = 44/13`
Vậy `D = 44/13`