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Can someone solve this question ~
[tex]\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}[/tex]
[tex]\boxed{\boxed{Step \: by \: step \: explanation \: required~}}\ [/tex]
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Answer :

[tex]\\ \sf{:}\Rrightarrow {\displaystyle{\lim_{x\to -3}}}\dfrac{x^2-9}{x^2+2x-3}[/tex]

[tex]\\ \sf{:}\Rrightarrow {\displaystyle{\lim_{x\to -3}}}\dfrac{(x+3)(x-3)}{x^2+3x-x-3}[/tex]

[tex]\\ \sf{:}\Rrightarrow {\displaystyle{\lim_{x\to -3}}}\dfrac{\cancel{(x+3)}(x-3)}{\cancel{(x+3)}(x-1)}[/tex]

[tex]\\ \sf{:}\Rrightarrow {\displaystyle{\lim_{x\to -3}}}\dfrac{x-3}{x-1}[/tex]

  • Apply limits

[tex]\\ \sf{:}\Rrightarrow \dfrac{-3-3}{-3-1}[/tex]

[tex]\\ \sf{:}\Rrightarrow \dfrac{-6}{-4}[/tex]

[tex]\\ \sf{:}\Rrightarrow \dfrac{3}{2}[/tex]

Hope you could understand.

If you have any query, feel free to ask.

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