SOLUTION
Given question 3 in the image, the following are the solution steps to answer the question.
STEP 1: Write the given expression
[tex](-\frac{4}{5}t+\frac{5}{3}s)+(-3-\frac{7}{5}s+2t)[/tex]
STEP 2: To simplify the expressions, Use the distributive property to open the brackets
[tex]\begin{gathered} (-\frac{4}{5}t+\frac{5}{3}s)+(-3-\frac{7}{5}s+2t) \\ +\times-=- \\ We\text{ have:} \\ -\frac{4}{5}t+\frac{5}{3}s-3-\frac{7}{5}s+2t \end{gathered}[/tex]
STEP 3: Collect like terms
[tex]-\frac{4}{5}t+2t+\frac{5}{3}s-\frac{7}{5}s-3[/tex]
STEP 4: Subtract the t part
[tex]\begin{gathered} -\frac{4}{5}t+2t=(-\frac{4}{5}+2)t \\ -\frac{4}{5}+2=-\frac{4}{5}+\frac{2}{1}----LCM=5 \\ \Rightarrow\frac{-(1\times4)+(5\times2)}{5}=\frac{-4+10}{5}=\frac{6}{5} \\ -\frac{4}{5}t+2t=\frac{6}{5}t \end{gathered}[/tex]
STEP 5: Subtract the s part of the expression in Step 3
[tex]\begin{gathered} \frac{5}{3}s-\frac{7}{5}s=(\frac{5}{3}-\frac{7}{5})s \\ (\frac{5}{3}-\frac{7}{5})----\text{LCM is 15} \\ \Rightarrow\frac{(5\times5)-(3\times7)}{15}=\frac{25-21}{15}=\frac{4}{15} \\ \frac{5}{3}s-\frac{7}{5}s=\frac{4}{15}s \end{gathered}[/tex]
STEP 6: Rewrite the expressions gotten to produce the final expression
[tex]\begin{gathered} \text{Substituting the derived value for the t part and the s part, we have:} \\ \mleft(-\frac{4}{5}t+\frac{5}{3}s\mright)+\mleft(-3-\frac{7}{5}s+2t\mright)=\frac{6}{5}t+\frac{4}{15}s-3 \\ \end{gathered}[/tex]
Hence, the final expression from adding the two expressions are:
[tex]\frac{6}{5}t+\frac{4}{15}s-3[/tex]
