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Question Number 127933 by AgnibhoMukhopadhyay last updated on 03/Jan/21

(1/((1/(x − 3)) + (1/(x + 4)))) If x > 0 and x ≠ 3, which of the following is equivalent to the expresion above? A. 2x + 1 B. x^2 + x − 12 C. ((x^2 + x − 12)/(2x + 1)) D. ((2x + 1)/(x^2 + x −12))

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{\frac{\mathrm{1}}{{x}\:−\:\mathrm{3}}\:+\:\frac{\mathrm{1}}{{x}\:+\:\mathrm{4}}} \\ $$ $$ \\ $$ $$\mathrm{If}\:{x}\:>\:\mathrm{0}\:\mathrm{and}\:{x}\:\neq\:\mathrm{3},\:\mathrm{which}\:\mathrm{of}\:\mathrm{the}\:\:\: \\ $$ $$\mathrm{following}\:\mathrm{is}\:\mathrm{equivalent}\:\mathrm{to}\:\mathrm{the}\: \\ $$ $$\mathrm{expresion}\:\mathrm{above}? \\ $$ $$\mathrm{A}.\:\:\mathrm{2}{x}\:+\:\mathrm{1} \\ $$ $$\mathrm{B}.\:\:{x}^{\mathrm{2}} \:+\:{x}\:−\:\mathrm{12}\: \\ $$ $$\mathrm{C}.\:\:\frac{{x}^{\mathrm{2}} \:+\:{x}\:−\:\mathrm{12}}{\mathrm{2}{x}\:+\:\mathrm{1}} \\ $$ $$\mathrm{D}.\:\:\frac{\mathrm{2}{x}\:+\:\mathrm{1}}{{x}^{\mathrm{2}} \:+\:{x}\:−\mathrm{12}} \\ $$

Answered by bramlexs22 last updated on 03/Jan/21

(1/((2x+1)/(x^2 +x−12))) = ((x^2 +x−12)/(2x+1))

$$\frac{\mathrm{1}}{\frac{\mathrm{2x}+\mathrm{1}}{\mathrm{x}^{\mathrm{2}} +\mathrm{x}−\mathrm{12}}}\:=\:\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{x}−\mathrm{12}}{\mathrm{2x}+\mathrm{1}}\: \\ $$

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