Simplifying a ratio of linear polynomials: \( 1,-1 \), and no simplification For each expression, simplify if possible. If applicable, click on "Cannot be simplified". \[ \begin{array}{l}\frac{2 v+5}{5+2 v}=\square \\ \frac{4-3 v}{3 v-4}\end{array}=\square \]

We begin by examining the two expressions. 1) For the expression (2v + 5)/(5 + 2v):  Notice that 5 + 2v is just a rearrangement of 2v + 5. In other words, they are identical.  Thus, (2v + 5)/(5 + 2v) simplifies to 1. 2) For the expression (4 – 3v)/(3v – 4):  Observe that 4 – 3v can be rewritten as –(3v – 4) because   4 – 3v = –1 × (3v – 4).  Therefore, (4 – 3v)/(3v – 4) becomes –(3v – 4)/(3v – 4).  Cancelling the common (3v – 4) (assuming 3v – 4 ≠ 0) leaves –1. The simplified forms are:  (2v + 5)/(5 + 2v) = 1   and  (4 – 3v)/(3v – 4) = –1.