Prove the sum of two rational numbers is rational where a, b, c, and d are integers and b and d cannot be zero.

steps reasons
1. a over b plus c over d given
2. ad over bd plus cb over bd
3. ad plus cb all over bd simplify

fill in the missing reason in the proof.
multiply to get a common denominator.
add to get a common denominator.
distribute d to all terms.
add d to all terms

Demonstrate the proof of your new polynomial identity through an algebraic proof and a numerical proof in an engaging way! make it so the whole world wants to purchase your polynomial identity and can't imagine living without it! you must: label and display your new polynomial identity prove that it is true through an algebraic proof, identifying each step demonstrate that your polynomial identity works on numerical relationships create your own using the columns below. see what happens when different binomials or trinomials are combined. square one factor from column a and add it to one factor from column b to develop your own identity. column a column b (x − y) (x2 + 2xy + y2) (x + y) (x2 − 2xy + y2) (y + x) (ax + b) (y − x) (cy + d)

Write the sentence as an equation. 6 fewer than the quantity 140 times j equals 104

What are the coordinates of the point is 1/4 of the way from a (-6, -3) to b (6, 1)? a. (-3, -2) b. (0, -2) c. (-1, 0) d. (3, 2)