((v^2-2v-3)/(v^2-7v+10))((2v-10)/(5v+5))

Jasonbradley

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Jun 16, 2024

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Simplifying Rational Expressions

This article will guide you through simplifying the expression:

((v^2-2v-3)/(v^2-7v+10))((2v-10)/(5v+5))

Step 1: Factor the Expressions

Begin by factoring each of the quadratic expressions and binomials:

• v^2-2v-3: This factors to (v-3)(v+1)
• v^2-7v+10: This factors to (v-5)(v-2)
• 2v-10: This factors to 2(v-5)
• 5v+5: This factors to 5(v+1)

Now, our expression looks like this:

((v-3)(v+1)/((v-5)(v-2)))((2(v-5))/(5(v+1)))

Step 2: Simplify by Cancelling Common Factors

We can now cancel out common factors present in both the numerator and denominator:

• (v+1) appears in both the numerator and denominator
• (v-5) appears in both the numerator and denominator

This leaves us with:

(v-3)/(v-2) * 2/5

Step 3: Final Result

Finally, we multiply the remaining factors:

(2(v-3))/(5(v-2))

Therefore, the simplified form of the expression ((v^2-2v-3)/(v^2-7v+10))((2v-10)/(5v+5)) is (2(v-3))/(5(v-2)).

Important Note: Remember that this simplified expression is only valid when v ≠ 2 and v ≠ -1, as these values would make the original expression undefined.