Question : Simplify the expression: $\frac{143 \times 143+143 \times 139+139 \times 139}{143 \times 143 \times 143-139 \times 139 \times 139}$
Option 1: $\frac{1}{2}$
Option 2: $282$
Option 3: $\frac{1}{4}$
Option 4: $4$
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Correct Answer: $\frac{1}{4}$
Solution : Given: $\frac{143 \times 143+143 \times 139+139 \times 139}{143 \times 143 \times 143-139 \times 139 \times 139}$ $=\frac{(143)^2+143\times139+(139)^2}{(143)^3-(139)^3}$ We know, $a^3-b^3=(a-b)(a^2+ab+b^2)$ $=\frac{(143)^2+143\times139+(139)^2}{(143-139)((143)^2+143\times139+(139)^2)}$ $=\frac{1}{143-139}$ $=\frac{1}{4}$ Hence, the correct answer is $\frac{1}{4}$.
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Question : Find the value of the given expression: $\frac{(4\frac{1}{3}+3\frac{1}{3}\times 1\frac{4}{5}\div 3\frac{3}{4}\times (1\frac{1}{2}+1\frac{1}{3}))}{(\frac{2}{3}\div \frac{5}{6}\times \frac{2}{3})}$
Option 1: $11 \frac{3}{8}$
Option 2: $10\frac{1}{8}$
Option 3: $14\frac{3}{8}$
Option 4: $16\frac{5}{8}$
Question : Simplify the following expression. $\frac{(0.96 \times 0.96 \times 0.96+0.04 \times 0.04 \times 0.04)}{(0.96 \times 0.96-0.96 \times 0.04+0.04 \times 0.04)}$
Option 1: 0
Option 2: 0.82
Option 3: 2
Option 4: 1
Question : Simplify the given expression: $\frac{(0.25)^4+2×(0.25)^2+1–(0.25)^2}{(0.25)^2+0.25+1}$
Option 1: 0.6755
Option 2: 0.9025
Option 3: 0.8125
Option 4: 0.7835
Question : Simplify the given expression. $\frac{0.24 \times 0.24 \times 0.24-0.008}{0.24 \times 0.24+0.048+0.04}$
Option 1: 0.04
Option 2: 0.02
Option 3: 0.01
Option 4: 0.03
Question : Simplify the expression: $\frac{1}{8}\left[\frac{1}{b-1}-\frac{1}{b+1}-\frac{2}{b^2+1}-\frac{4}{b^4+1}\right]$
Option 1: $\frac{1}{b^8-1}$
Option 2: $\frac{8}{b^8+1}$
Option 3: $\frac{8}{b^8-1}$
Option 4: $\frac{1}{b^8+1}$
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