3.4P: Practice

MTH 95: Algebra 3 · LibreTexts

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    From LibreTexts, under CC BY-NC 4.0, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    Practice Makes Progress

    Add or subtract the rational expressions, as indicated, and simplify your answer. State all restrictions.

    Exercise

    \(\dfrac{7x^2−49x}{x−6}+\dfrac{42}{x−6}\)

    Exercise

    \(\dfrac{9x^2}{x−1}+\dfrac{72x−63}{1−x}\)

    Exercise

    \(\dfrac{4x^2−60x}{x−7}+\dfrac{224}{x−7}\)

    Exercise

    \(\dfrac{3x^2}{x−2}−\dfrac{48−30x}{2−x}\)

    Exercise

    \(\dfrac{3x}{x^2−6x+5}+\dfrac{15}{x^2−14x+45}\)

    Exercise

    \(\dfrac{5x}{x^2−21x+98}−\dfrac{35}{7x−x^2}\)

    Exercise

    \(\dfrac{−7x}{x^2−8x+15}−\dfrac{35}{x^2−12x+35}\)

    Exercise

    \(\dfrac{−9x}{x^2−6x+8}−\dfrac{18}{x^2−2x}\)

    Exercise

    \(\dfrac{8x}{5x−x^2}+\dfrac{120}{x^2+5x−50}\)

    Self-Check

    In this section, you practiced:

    1. Identifying least common denominators (LCD)
    2. Completing addition or subtraction of two rational expressions with the same denominator
    3. Completing addition or subtraction of two rational expressions with different denominators using the LCD
    4. Identifying excluded values of a rational expression

    From the list of skills above:

    1. I can complete these independently without notes:
    1. I can complete these, but need to reference an example or other resource to help:
    1. I don’t understand these yet:

    It’s okay to not be fully confident with every skill yet! But it’s essential to continue making progress. Identify at least one step you will take to improve your understanding of the topics you listed in parts 2 or 3 above:

    • Visit the math lab
    • Contact my instructor
    • Re-work practice problems
    • Ask a classmate or friend for help

    Which step(s) from above did you complete after last week's textbook practice?

    This page titled 3.4P: Practice was last modified on Wed, 10 Dec 2025 03:00:28 GMT and is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Math Department.