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SSC Selection Post 2022 PYQ — Question 53

SSC Selection Post - Higher Secondary Level - 14 March 2022 - Shift 2 • Quantitative Aptitude • Q53

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Simplify the given expression:

((a+x)(ax2−x3)a3+x3×a2−ax+x2a2x2+x4)÷(a2−2ax+x2)(a−x)(a4−x4),a≠x({(a+x) (ax^2-x^3) \over a^3 + x^3} \times {a^2-ax+x^2 \over a^2x^2 + x^4}) \div {(a^2-2ax+x^2) (a - x) \over (a^4 - x^4)}, a \neq x

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Correct answer: A

Explanation

The correct answer is option 1 i.e. a+xa−x{a + x \over a - x}.

((a+x)(ax2−x3)a3+x3×a2−ax+x2a2x2+x4)÷(a2−2ax+x2)(a−x)(a4−x4)({(a+x) (ax^2-x^3) \over a^3 + x^3} \times {a^2-ax+x^2 \over a^2x^2 + x^4}) \div {(a^2-2ax+x^2) (a - x) \over (a^4 - x^4)}

⇒ ((a+x)(ax2−x3)(a+x)(a2+x2−ax)×(a2−ax+x2)x2(a2+x2))÷(a−x)2(a−x)(a−x)(a+x)(a2+x2)({(a+x) (ax^2-x^3) \over (a+x)(a^2+x^2-ax)} \times {(a^2-ax+x^2) \over x^2(a^2 + x^2)}) \div {(a-x)^2(a-x)\over (a-x)(a+x)(a^2+x^2)}

⇒ (ax2−x3)x2(a2+x2)÷(a−x)2(a+x)(a2+x2) {(ax^2-x^3) \over x^2(a^2 + x^2)} \div {(a-x)^2\over(a+x)(a^2+x^2)}

⇒​​​​​​​ (ax2−x3)x2(a2+x2)×(a+x)(a2+x2)(a−x)2 {(ax^2-x^3) \over x^2(a^2 + x^2)} \times {(a+x)(a^2+x^2)\over(a-x)^2}

⇒​​​​​​​ x2(a−x)x2×(a+x)(a−x)2 {x^2(a-x) \over x^2} \times {(a+x)\over(a-x)^2} = (a+x)(a−x){(a+x)\over(a-x)}