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Original
2026-01-01
Modified
2026-02-28
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<p>Variables are usually represented by letters like a, b, c, x, y, z, etc. They represent changeable or unknown values.</p>
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<p>Variables are usually represented by letters like a, b, c, x, y, z, etc. They represent changeable or unknown values.</p>
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<p><strong>Step 1:</strong>Factor both the numerator and the denominator, including variables.</p>
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<p><strong>Step 1:</strong>Factor both the numerator and the denominator, including variables.</p>
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<p><strong>Step 2</strong>: Avoid all common factors from the numerator and the denominator.</p>
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<p><strong>Step 2</strong>: Avoid all common factors from the numerator and the denominator.</p>
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<p><strong>Step 3:</strong>The resultant is in simple form.</p>
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<p><strong>Step 3:</strong>The resultant is in simple form.</p>
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<p>An example will help us understand better: </p>
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<p>An example will help us understand better: </p>
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<p>Find the simplest form of the fraction \(\frac{6x^2y}{3xy^2} \)</p>
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<p>Find the simplest form of the fraction \(\frac{6x^2y}{3xy^2} \)</p>
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<p><strong>Step 1:</strong>Numerator = 6x2y</p>
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<p><strong>Step 1:</strong>Numerator = 6x2y</p>
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<p>The prime factorization of 6 is \(2 × 3\). </p>
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<p>The prime factorization of 6 is \(2 × 3\). </p>
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<p>Therefore, \(6 = 2 × 3\)</p>
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<p>Therefore, \(6 = 2 × 3\)</p>
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<p>Similarly, the prime factorization of x2 is x × x </p>
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<p>Similarly, the prime factorization of x2 is x × x </p>
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<p>So,\( x^2 = x × x \)</p>
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<p>So,\( x^2 = x × x \)</p>
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<p>y can be written as it is.</p>
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<p>y can be written as it is.</p>
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<p>In other words, \(6x^2y = 2 × 3 × x × x × y.\)</p>
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<p>In other words, \(6x^2y = 2 × 3 × x × x × y.\)</p>
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<p>Let’s do the same in the denominator.</p>
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<p>Let’s do the same in the denominator.</p>
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<p>Denominator = 3xy2</p>
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<p>Denominator = 3xy2</p>
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<p>Since 3 is a prime number, it cannot be factorized further. So write 3 as it is. </p>
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<p>Since 3 is a prime number, it cannot be factorized further. So write 3 as it is. </p>
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<p>\(x = x\)</p>
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<p>\(x = x\)</p>
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<p>\(y^2 = y × y \)</p>
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<p>\(y^2 = y × y \)</p>
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<p>So \(3xy^2 = 3 × x × y × y\)</p>
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<p>So \(3xy^2 = 3 × x × y × y\)</p>
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<p><strong>Step 2:</strong>Let’s rewrite the fraction and then cancel out the common factors.</p>
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<p><strong>Step 2:</strong>Let’s rewrite the fraction and then cancel out the common factors.</p>
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<p>\(6x^2y = 2 × 3 × x × x × y\) and \(3xy^2 = 3 × x × y × y \)</p>
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<p>\(6x^2y = 2 × 3 × x × x × y\) and \(3xy^2 = 3 × x × y × y \)</p>
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<p>Therefore, the fraction is \(\frac{2 \times 3 \times x \times x \times y}{3 \times x \times y \times y} \)</p>
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<p>Therefore, the fraction is \(\frac{2 \times 3 \times x \times x \times y}{3 \times x \times y \times y} \)</p>
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<p>Now, canceling out common factors (x, y, 3)</p>
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<p>Now, canceling out common factors (x, y, 3)</p>
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<p>x → \(\frac{2 \times x \times y}{y \times y} \)</p>
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<p>x → \(\frac{2 \times x \times y}{y \times y} \)</p>
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<p>y → \(\frac{2x}{y} \), we get: </p>
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<p>y → \(\frac{2x}{y} \), we get: </p>
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<p>\(\frac{2x}{y} \).</p>
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<p>\(\frac{2x}{y} \).</p>
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