Question - Simplifying Rational Expression
mathsimplify rational expressionsfactoring numerator and denominatordifference of squares rulequadratic trinomial factoring
Solution:
To simplify the given expression, you should recognize that the numerator can be factored using the difference of squares rule, and the denominator appears to be already factored. Here is the step-by-step simplification:The given expression is $$\dfrac{x^2 - 16}{x^2 - 3x - 28}$$.Factor the numerator which is a difference of squares:$$\dfrac{(x + 4)(x - 4)}{x^2 - 3x - 28}$$.Now let's factor the denominator. To factor a quadratic trinomial, we look for two numbers that multiply to the constant term (-28) and add to the linear coefficient (-3). Those two numbers are -7 and +4.$$\dfrac{(x + 4)(x - 4)}{(x - 7)(x + 4)}$$.Now, the $$(x + 4)$$ term is both in the numerator and the denominator, so they can be canceled out:$$\dfrac{x - 4}{x - 7}$$.The expression is now simplified to:$$x - 4 \over x - 7$$,which cannot be simplified further.
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