Answered

Get the answers you need at Westonci.ca, where our expert community is dedicated to providing you with accurate information. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform. Get quick and reliable solutions to your questions from a community of experienced experts 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]
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.