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<ol class="abc-list"><li data-list-item-id="t6-q33-source-item-a" data-list-item-path="t6-q33-source-item-a"><div class="list-item-paragraph">Express $\frac{x-3}{x^2-6x+9}-\frac1{x+3}+\frac4{9-x^2}$ as a single fraction in lowest terms.</div></li><li data-list-item-id="t6-q33-source-item-b" data-list-item-path="t6-q33-source-item-b"><div class="list-item-paragraph">Simplify $\frac{18a^5b^7(x^4+y^4)}{12a^{-2}b^3(x^8-y^8)}$.</div></li></ol>

Express $\frac{x-3}{x^2-6x+9}-\frac1{x+3}+\frac4{9-x^2}$ as a single fraction in lowest terms.

Simplify $\frac{18a^5b^7(x^4+y^4)}{12a^{-2}b^3(x^8-y^8)}$.

Multiplication and Division of Algebraic Fractions involving Factorisation

Advanced fraction and index simplification

Algebraic Expressions, Identities and Formulae

Simplify $\frac{{{p}^{2}}+3p+2}{2(p+1)}\div \frac{{{p}^{2}}-4}{3p}$.

Simplify $\frac{{{p}^{2}}+3p+2}{2(p+1)}\div \frac{{{p}^{2}}-4}{3p}$.

Factorising Quadratics to Simplify a Rational Expression

Simplify $\frac{5{{(x-2)}^{2}}}{9{{x}^{2}}-6{{x}^{3}}}\div \frac{6{{x}^{2}}-24}{21x-14{{x}^{2}}}$.

Simplify $\frac{5{{(x-2)}^{2}}}{9{{x}^{2}}-6{{x}^{3}}}\div \frac{6{{x}^{2}}-24}{21x-14{{x}^{2}}}$.

Algebra: Dividing Polynomial Fractions

Simplify $\frac{{{a}^{2}}+a-12}{8a+12b}\times \frac{14a+21b}{{{a}^{2}}+2a-8}$.

Simplify $\frac{{{a}^{2}}+a-12}{8a+12b}\times \frac{14a+21b}{{{a}^{2}}+2a-8}$.

Factorising and Cancelling in Rational Expressions

Simplify $\frac{4a+1}{4a-1}\times \frac{{{(4a-1)}^{2}}}{32{{a}^{2}}-2}$.

Simplify $\frac{4a+1}{4a-1}\times \frac{{{(4a-1)}^{2}}}{32{{a}^{2}}-2}$.

Algebra: Simplifying Products of Polynomial Fractions

Simplify $\frac{{{x}^{2}}-16}{6-2x}\times \frac{6}{x+4}$.

Simplify $\frac{{{x}^{2}}-16}{6-2x}\times \frac{6}{x+4}$.

Algebra: Simplifying Products of Rational Expressions

Simplify $\frac{{{(5-3a)}^{2}}}{9{{a}^{2}}c}\div \frac{25-9{{a}^{2}}}{12abc}$.

Simplify $\frac{{{(5-3a)}^{2}}}{9{{a}^{2}}c}\div \frac{25-9{{a}^{2}}}{12abc}$.

Algebra: Dividing Fractions with Polynomial Terms

Simplify $\frac{18x-3xy}{4{{x}^{2}}}\div \frac{30-5y}{2xy}$.

Simplify  $\frac{18x-3xy}{4{{x}^{2}}}\div \frac{30-5y}{2xy}$.

Algebra: Dividing Algebraic Fractions

Simplify $\frac{3x}{3x+3}\times \frac{6{{x}^{2}}+6x}{4{{x}^{2}}}$.

Simplify $\frac{3x}{3x+3}\times \frac{6{{x}^{2}}+6x}{4{{x}^{2}}}$.

Simplify $\frac{2x}{{{x}^{2}}-x-6}\div \frac{2x-6}{x+2}$ .

Simplify $\frac{2x}{{{x}^{2}}-x-6}\div \frac{2x-6}{x+2}$ .

Factorising Quadratics to Simplify a Fraction

Simplify $\frac{7y+3}{{{(5y-4)}^{2}}}\times \frac{15y-12}{3}$.

Simplify $\frac{7y+3}{{{(5y-4)}^{2}}}\times \frac{15y-12}{3}$.

Simplifying Algebraic Fractions (Multiplication)

Simplify $\frac{2{{x}^{2}}-2}{{{x}^{2}}+2x+1}\div \frac{1}{x+1}$.

Simplify $\frac{2{{x}^{2}}-2}{{{x}^{2}}+2x+1}\div \frac{1}{x+1}$.

Indices and Factorisation in Fraction Simplification

Simplify $\frac{1}{2t-4}\times \frac{6+t-2{{t}^{2}}}{1-t}$.

Simplify $\frac{1}{2t-4}\times \frac{6+t-2{{t}^{2}}}{1-t}$.

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