Question

How do you do number #3 I need help quick because it’s due today by 11:30…. So please help meeeeeeeeee

Answer 1

Given question 3 in the image, the following are the solution steps to answer the question.

STEP 1: Write the given expression

`(-(4)/(5)t+(5)/(3)s)+(-3-(7)/(5)s+2t)`

STEP 2: To simplify the expressions, Use the distributive property to open the brackets

`\begin{gathered} (-(4)/(5)t+(5)/(3)s)+(-3-(7)/(5)s+2t) \\ +*-=- \\ We\text{ have:} \\ -(4)/(5)t+(5)/(3)s-3-(7)/(5)s+2t \end{gathered}`

STEP 3: Collect like terms

`-(4)/(5)t+2t+(5)/(3)s-(7)/(5)s-3`

STEP 4: Subtract the t part

`\begin{gathered} -(4)/(5)t+2t=(-(4)/(5)+2)t \\ -(4)/(5)+2=-(4)/(5)+(2)/(1)----LCM=5 \\ \Rightarrow(-(1*4)+(5*2))/(5)=(-4+10)/(5)=(6)/(5) \\ -(4)/(5)t+2t=(6)/(5)t \end{gathered}`

STEP 5: Subtract the s part of the expression in Step 3

`\begin{gathered} (5)/(3)s-(7)/(5)s=((5)/(3)-(7)/(5))s \\ ((5)/(3)-(7)/(5))----\text{LCM is 15} \\ \Rightarrow((5*5)-(3*7))/(15)=(25-21)/(15)=(4)/(15) \\ (5)/(3)s-(7)/(5)s=(4)/(15)s \end{gathered}`

STEP 6: Rewrite the expressions gotten to produce the final expression

`\begin{gathered} \text{Substituting the derived value for the t part and the s part, we have:} \\ \mleft(-(4)/(5)t+(5)/(3)s\mright)+\mleft(-3-(7)/(5)s+2t\mright)=(6)/(5)t+(4)/(15)s-3 \\ \end{gathered}`

Hence, the final expression from adding the two expressions are:

`(6)/(5)t+(4)/(15)s-3`