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- https://math.libretexts.org/Courses/Coastline_College/Math_C097%3A_Support_for_Precalculus_Corequisite%3A_MATH_C170/1.02%3A_Algebra_Support/1.2.13%3A_Simplifying_Multiplying_and_Dividing_Rational_Expressions\(\boldsymbol{\begin{array} {ll} &\dfrac{3a^2−8a−3}{a^2−25}·\dfrac{a^2+10a+25}{3a^2−14a−5} \\ & \\ \begin{array} {ll} \text{Factor the numerators and denominators} \\ \text{and then multiply.} \end{array}} &\dfrac...\(\boldsymbol{\begin{array} {ll} &\dfrac{3a^2−8a−3}{a^2−25}·\dfrac{a^2+10a+25}{3a^2−14a−5} \\ & \\ \begin{array} {ll} \text{Factor the numerators and denominators} \\ \text{and then multiply.} \end{array}} &\dfrac{(3a+1)(a−3)(a+5)(a+5)}{(a−5)(a+5)(3a+1)(a−5)} \\ & \\ Simplify by dividing outcommon factors. &\dfrac{\cancel{(3a+1)}(a−3)\cancel{(a+5)}(a+5)}{(a−5)\cancel{(a+5)}\cancel{(3a+1)}(a−5)} \\ & \\ \text{Simplify.} &\dfrac{(a−3)(a+5)}{(a−5)(a−5)} \\ & \\ \…
- https://math.libretexts.org/Bookshelves/Precalculus/Corequisite_Companion_to_Precalculus_(Freidenreich)/5%3A_Rational_Expression/5.01%3A_Simplify_Rational_ExpressionsRational numbers are sometimes informally called fractions. Numbers such as 3/4 and −1/5 are rational numbers. When simplifying rational expressions, look for groups of variables or numbers that c...Rational numbers are sometimes informally called fractions. Numbers such as 3/4 and −1/5 are rational numbers. When simplifying rational expressions, look for groups of variables or numbers that can be canceled to one. Cancel as many times as permits within a rational expression.
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Calculus_for_Business_and_Social_Sciences_Corequisite_Workbook_(Dominguez_Martinez_and_Saykali)/09%3A_Rational_Expressions/9.01%3A_Simplify_Rational_ExpressionsTo simplify a rational expression, factor both the numerator and the denominator, and remove common factors from both the numerator and the denominator. A simplified rational expression has only one d...To simplify a rational expression, factor both the numerator and the denominator, and remove common factors from both the numerator and the denominator. A simplified rational expression has only one division, and a single numerator and denominator. If the expressions cannot be factored, then the rational expression cannot be simplified.
- https://math.libretexts.org/Courses/Highline_College/MATHP_141%3A_Corequisite_Precalculus/02%3A_Algebra_Support/2.13%3A_Simplifying_Multiplying_and_Dividing_Rational_Expressions\(\boldsymbol{\begin{array} {ll} &\dfrac{3a^2−8a−3}{a^2−25}·\dfrac{a^2+10a+25}{3a^2−14a−5} \\ & \\ \begin{array} {ll} \text{Factor the numerators and denominators} \\ \text{and then multiply.} \end{array}} &\dfrac...\(\boldsymbol{\begin{array} {ll} &\dfrac{3a^2−8a−3}{a^2−25}·\dfrac{a^2+10a+25}{3a^2−14a−5} \\ & \\ \begin{array} {ll} \text{Factor the numerators and denominators} \\ \text{and then multiply.} \end{array}} &\dfrac{(3a+1)(a−3)(a+5)(a+5)}{(a−5)(a+5)(3a+1)(a−5)} \\ & \\ Simplify by dividing outcommon factors. &\dfrac{\cancel{(3a+1)}(a−3)\cancel{(a+5)}(a+5)}{(a−5)\cancel{(a+5)}\cancel{(3a+1)}(a−5)} \\ & \\ \text{Simplify.} &\dfrac{(a−3)(a+5)}{(a−5)(a−5)} \\ & \\ \…
