Answered

Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Join our Q&A platform and get accurate answers to all your questions from professionals across multiple disciplines. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

x^2 + x - 6 over x^2 - 7x + 10
simplify fully

Sagot :

RedRicin
[tex]\frac{x^2+x-6}{x^2-7x+10}[/tex]

When you factor a quadratic ax² + bx + c, it becomes (x+m)(x+n), where mn = ac, and m+n = b.

In x²+x-6, we want to find two numbers that multiply to -6 and add to 1.
3 and -2 satisfy both of these criteria, so there are our factors.

[tex]\frac{(x+3)(x-2)}{x^2-7x+10}[/tex]

In x²-7x+10, we want to find two numbers that multiply to 10 and add to -7.
-5 and -2 satisfy both of these criteria, so there are our factors.

[tex]\frac{(x+3)(x-2)}{(x-5)(x-2)}[/tex]

The (x-2) cancels and we're left with

[tex]\boxed{\frac{x+3}{x-5}}[/tex]
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.