1"use strict"; 2!function(){try{var e="undefined"!=typeof window?window:"undefined"!=typeof global?global:"undefined"!=typeof globalThis?globalThis:"undefined"!=typeof self?self:{},n=(new e.Error).stack;n&&(e._sentryDebugIds=e._sentryDebugIds||{},e._sentryDebugIds[n]="46da70be-ae65-5e6c-837c-8537d2ae5194")}catch(e){}}(); 3(self.webpackChunk_N_E=self.webpackChunk_N_E||[]).push([[75666],{75666:(x,e,n)=>{n.r(e),n.d(e,{default:()=>i});let i={meta:{revision:"2026-09-09-plain-language",id:"ip-emaths-algebraic-fractions-surds",title:"Algebraic Fractions Quiz",subtitle:"Upper Secondary Mathematics ⢠simplifying and solving algebraic fractions",adminLabel:"IP EMaths - Algebraic Fractions"},mcqQuestions:[{id:3,question:"For the expression 1 / (x - 4), which restriction is required?",options:["\\(x \\ne 1\\)","\\(x \\ne -4\\)","\\(x \\ne 4\\)","x > 4"],correct:2,explanation:"The denominator cannot be zero, so \\(x - 4 \\ne 0\\)."},{id:1,question:"Simplify \\(6x / 3x^2\\) for \\(x \\ne 0\\).",options:["2x","2/x","3/x","x/2"],correct:1,explanation:"\\(6x / 3x^2 = 2 / x\\) after cancelling a common factor of \\(3x\\)."},{id:2,question:"Simplify \\((x^2 - 9) / (x - 3)\\), given \\(x \\ne 3\\).",options:["x - 3","x + 3","x^2 + 3","x^2 - 3"],correct:1,explanation:"\\(x^2 - 9 = (x - 3)(x + 3)\\), so the expression simplifies to \\(x + 3\\)."},{id:5,question:"Simplify \\((x^2 + 5x + 6) / (x^2 - 4)\\), given \\(x \\ne \\pm 2\\).",options:["(x + 2)/(x - 2)","(x + 3)/(x - 2)","(x + 3)/(x + 2)","(x - 3)/(x - 2)"],correct:1,explanation:"\\(x^2 + 5x + 6 = (x + 2)(x + 3)\\) and \\(x^2 - 4 = (x + 2)(x - 2)\\), so the result is \\((x + 3)/(x - 2)\\)."},{id:4,question:"Simplify 2/(x - 1) - 3/(x + 2).",options:["(x + 1) / ((x - 1)(x + 2))","(7 - x) / ((x - 1)(x + 2))","(x - 7) / (x^2 + 1)","(5x + 1) / ((x - 1)(x + 2))"],correct:1,explanation:"Using a common denominator gives \\([2(x + 2) - 3(x - 1)] / [(x - 1)(x + 2)] = (7 - x) / [(x - 1)(x + 2)]\\)."},{id:6,question:"Solve \\(1/x + 1/2 = 3/4\\).",options:["\\(x = 2\\)","\\(x = 3\\)","\\(x = 4\\)","\\(x = 8\\)"],correct:2,explanation:"\\(1/x = 3/4 - 1/2 = 1/4\\), so \\(x = 4\\)."}],openEndedQuestions:[{id:1,question:"Combine 3/x + 2/(x + 1) into a single fraction and state any restrictions on x.",markingPoints:["Using denominator \\(x(x + 1)\\), the result is \\([3(x + 1) + 2x] / [x(x + 1)] = (5x + 3) / [x(x + 1)]\\), with \\(x \\ne 0\\) and \\(x \\ne -1\\)."]},{id:2,question:"Explain why cancelling is valid for common factors but not for separate terms. Use (x^2 - 9)/(x - 3) as an example.",markingPoints:["You may cancel only factors. Since x^2 - 9 factorises to (x - 3)(x + 3), the common factor x - 3 can be cancelled to give x + 3. You cannot cancel terms in x^2 - 9 directly because subtraction does not create a common factor."]}]}}}]); 4//# sourceMappingURL=75666.ed0a1baaeae63d48.js.map 5//# debugId=46da70be-ae65-5e6c-837c-8537d2ae5194
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