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f(x)=1/(3-x)+(-4x)/((3-x)(3+x))−6−5−4−3−2−10123456−3-2.5−2-1.5−1-0.500.511.522.53xy

Exercise

lim⁡x→1(13−x−4x(3−x)(3+x))\lim_{x\to1}\left(\frac{1}{3-x}-\frac{4x}{\left(3-x\right)\left(3+x\right)}\right)

Step-by-step Solution

Learn how to solve limits by direct substitution problems step by step online. Find the limit of 1/(3-x)+(-4x)/((3-x)(3+x)) as x approaches 1. The sum of two terms multiplied by their difference is equal to the square of the first term minus the square of the second term. In other words: (a+b)(a-b)=a^2-b^2.. Calculate the power \sqrt{9}. Any expression multiplied by 1 is equal to itself. Simplify \sqrt{x^2} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals \frac{1}{2}.
Find the limit of 1/(3-x)+(-4x)/((3-x)(3+x)) as x approaches 1

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Main Topic: Limits by Direct Substitution

Find limits of functions at a specific point by directly plugging the value into the function.

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limx→1(13−x −4x(3−x)(3+x) )
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