91Ó°ÊÓ

Perform each indicated operation. Simplify if possible. \(\frac{70}{m^{2}-100}+\frac{7}{2(m+10)}\)

Simplify each expression. Each exercise contains a four-term polynomial that should be factored by grouping. $$ \frac{x^{2}+x y+2 x+2 y}{x+2} $$

Write each phrase as an expression. The reciprocal of \(x\)

A manufacturer of cans of salted mixed nuts states that the ratio of peanuts to other nuts is 3 to 2 . If 324 peanuts are in a can, find how many other nuts should also be in the can.

If the distance formula \(d=r \cdot t\) is solved for \(t,\) ther \(t=\frac{d}{r} .\) Use this formula to find \(t\) if distance \(d\) is \(\frac{20 x}{3}\) miles and rate \(r\) is \(\frac{5 x}{9}\) miles per hour. Write \(t\) if simplified form.

Simplify each expression. Each exercise contains a four-term polynomial that should be factored by grouping. $$ \frac{a b+a c+b^{2}+b c}{b+c} $$

Perform the indicated operations. $$ \frac{12 x-6}{x^{2}+3 x} \cdot \frac{4 x^{2}+13 x+3}{4 x^{2}-1} $$

There are 1280 calories in a 14 -ounce portion of Eagle Brand Milk. Find how many calories are in 2 ounces of Eagle Brand Milk.

If the formula for the area of a rectangle, \(A=l \cdot w,\) is solved for \(w,\) then \(w=\frac{A}{l} .\) Use this formula to find \(w\) if area \(A\) is \(\frac{4 x-2}{3}\) square meters and length \(l\) is \(\frac{6 x-3}{5}\) meters. Write \(w\) in simplified form.

Write each phrase as an expression. The reciprocal of \(x+1\)