SOMEONE PLEASE HELP! Can someone show me how to work this out?

Mathematics

1 answer:

Vladimir [108]3 years ago

6 0

Answer:

2/(x+7)

Step-by-step explanation:

x²+5x-14 factors as (x-2)(x+7)

SO - multiply the fraction on the right by x+7 (both top and bottom)

Then both have the same denominator (x-2)(x+7), and the 1 becomes x+7.

Then you combine the fractions to make ((3x+3)-(x+7))/(x-2)(x+7).

This becomes (2x-4)/(x-2)(x+7).

You can factor the 2 out of the numerator for 2(x-2).

You now have 2(x-2)/(x-2)(x+7)

The (x-2)’s cancel out and you are left with

2/(x+7)

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What algebraic expression must be added to the sum of

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We need to add the expression: $4x^2-16$

Step-by-step explanation:

As the first step, add the first two polynomials listed in order to find what their sum is. Do such by combining like terms:

$3x^2+4x+8\,+ (2x^2-6x+3) =5x^2-2x+11$

now, you need to find another polynomial (let's call it P(x)) such that added to the one we just found above, will render $9x^2-2x-5$ as a result.

Putting this phrase in mathematical terms, we write:

$5x^2-2x+11\,+ P(x) = 9x^2-2x-5$

Now we solve for this unknown P(x) in this equation, by subtracting each of the terms that are accompanying it on the left side of the equation. We do one at a time for clarity:

$5x^2-2x+11\,+ P(x) = 9x^2-2x-5\\-2x+11+P(x)=9x^2-5x^2-2x-5\\-2x+11+P(x)=4x^2-2x-5\\11+P(x)=4x^2-2x+2x-5\\11+P(x)=4x^2-5\\P(x)=4x^2-5-11\\P(x)=4x^2-16$