AQA · Mathematics · 8300

GCSE Maths: Equations: fractional advanced

Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise for Equations: fractional advanced (Corbettmaths Video 111), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.

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  1. What is the first step when solving an equation like 3/(x+2) + 2/x = 1?

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    Find a common denominator (typically the product of the denominators) and rewrite all fractions with that denominator.

  2. Why must you multiply both sides of a fractional equation by the common denominator?

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    To eliminate the fractions and create a simpler polynomial equation that can be solved using standard algebraic techniques.

  3. In the equation 1/(x-10) + 2/(x-10) = 1, what simplification can you make before finding a common denominator?

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    Combine the fractions on the left side to get 3/(x-10) = 1, since they already have the same denominator.

  4. After eliminating fractions in a rational equation, what type of equation typically results?

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    Usually a quadratic equation (ax² + bx + c = 0), which can be solved by factoring or using the quadratic formula.

  5. What error was made in the step 7x + 14/x(x+2) - 2x/x(x+2) = 3?

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    The numerator 7(x+2) was incorrectly simplified. It should be (7x + 14)/[x(x+2)] with parentheses around the entire numerator, not 7x + 14/x(x+2).

  6. When solving fractional equations, what critical check should you perform on your final answers?

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    Check that no answer makes any denominator equal to zero, as those values would make the original equation undefined.

  7. For the equation 7/x - 2/(x+2) = 3, what is the common denominator?

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    x(x+2), which is the product of the two different denominators.

  8. In the equation 6/(x+1) - 1/(x+1) = 3, what value of x satisfies the equation?

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    x = 2/3. The left side simplifies to 5/(x+1) = 3, so 5 = 3(x+1), giving 5 = 3x + 3, then 2 = 3x.

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