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Add :-14\frac{1}{2} + 18\frac{3}{4} + 11\frac{2}{3} the right answer is 44\frac{11}{12}[/tex]please answer in steps

Answer» <html><body><p><strong>Answer:</strong></p><p></p><p><strong>Step-by-step explanation:</strong></p><p>We have studied procedures for working with fractions in earlier grades.</p><p></p><p> ab×cd=acbd(b≠0;d≠0)</p><p> ab+cb=a+cb(b≠0)</p><p> ab÷cd=ab×dc=adbc(b≠0;c≠0;d≠0)</p><p>Note: dividing by a fraction is the same as <a href="https://interviewquestions.tuteehub.com/tag/multiplying-2184915" style="font-weight:bold;" target="_blank" title="Click to know more about MULTIPLYING">MULTIPLYING</a> by the reciprocal of the fraction.</p><p></p><p>In some cases of simplifying an algebraic <a href="https://interviewquestions.tuteehub.com/tag/expression-980856" style="font-weight:bold;" target="_blank" title="Click to know more about EXPRESSION">EXPRESSION</a>, the expression will be a fraction. For <a href="https://interviewquestions.tuteehub.com/tag/example-978283" style="font-weight:bold;" target="_blank" title="Click to know more about EXAMPLE">EXAMPLE</a>,</p><p></p><p>x2+3xx+3</p><p>has a quadratic binomial in the numerator and a <a href="https://interviewquestions.tuteehub.com/tag/linear-1074458" style="font-weight:bold;" target="_blank" title="Click to know more about LINEAR">LINEAR</a> binomial in the denominator. We have to apply the different factorisation methods in order to factorise the numerator and the denominator before we can simplify the expression.</p><p></p><p>x2+3xx+3=x(x+3)x+3=x(x≠−3)</p><p>If x=−3 then the denominator, x+3=0 and the fraction is undefined.                                       <a href="https://interviewquestions.tuteehub.com/tag/worked-7256840" style="font-weight:bold;" target="_blank" title="Click to know more about WORKED">WORKED</a> EXAMPLE 18: SIMPLIFYING FRACTIONS</p><p>Simplify:</p><p>ax−b+x−abax2−abx,(x≠0;x≠b)</p><p>Use grouping to factorise the numerator and take out the common factor ax in the denominator</p><p>(ax−ab)+(x−b)ax2−abx=a(x−b)+(x−b)ax(x−b)</p><p>Take out common factor (x−b) in the numerator</p><p>=(x−b)(a+1)ax(x−b)</p><p>Cancel the common factor in the numerator and the denominator to give the final answer</p><p>=a+1ax</p><p>WORKED EXAMPLE 19: SIMPLIFYING FRACTIONS</p><p>Simplify:</p><p>x2−x−2x2−4÷x2+xx2+2x,(x≠0;x≠±2)</p><p>Factorise the numerator and denominator</p><p>=(x+1)(x−2)(x+2)(x−2)÷x(x+1)x(x+2)</p><p>Change the division sign and multiply by the reciprocal</p><p>=(x+1)(x−2)(x+2)(x−2)×x(x+2)x(x+1)</p><p>Write the final answer</p><p>=1</p><p>WORKED EXAMPLE 20: SIMPLIFYING FRACTIONS</p><p>Simplify:</p><p>x−2x2−4+x2x−2−x3+x−4x2−4,(x≠±2)</p><p>Factorise the denominators</p><p>x−2(x+2)(x−2)+x2x−2−x3+x−4(x+2)(x−2)</p><p>Make all denominators the same so that we can add or subtract the fractions</p><p>The lowest common denominator is (x−2)(x+2).</p><p></p><p>x−2(x+2)(x−2)+(x2)(x+2)(x+2)(x−2)−x3+x−4(x+2)(x−2)</p><p>Write as one fraction</p><p>x−2+(x2)(x+2)−(x3+x−4)(x+2)(x−2)</p><p>Simplify</p><p>x−2+x3+2x2−x3−x+4(x+2)(x−2)=2x2+2(x+2)(x−2)</p><p>Take out the common factor and write the final answer</p><p>2(x2+1)(x+2)(x−2)</p><p>WORKED EXAMPLE 21: SIMPLIFYING FRACTIONS</p><p>Simplify:</p><p>2x2−x+x2+x+1x3−1−xx2−1,(x≠0;x≠±1)</p><p>Factorise the numerator and denominator</p><p>2x(x−1)+(x2+x+1)(x−1)(x2+x+1)−x(x−1)(x+1)</p><p>Simplify and find the common denominator</p><p>2(x+1)+x(x+1)−x2x(x−1)(x+1)</p><p>Write the final answer</p><p>2x+2+x2+x−x2x(x−1)(x+1)=3x+2x(x−1)(x+1)</p><p></p></body></html>


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