NarcissaNyx
Answered

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Hi, could you help me with this substitution question?
I'd really appreciate if you added workings out as I'm terribly confused.
Thanks,

Hi Could You Help Me With This Substitution Question Id Really Appreciate If You Added Workings Out As Im Terribly Confused Thanks class=

Sagot :

semsee45

Answer:

[tex]-\dfrac{69}{14}[/tex]

Step-by-step explanation:

Substitute the given values of the variables into the given expression:

[tex]\implies \dfrac{60 \left(\dfrac{1}{3}\right)\left(-\dfrac{1}{5}\right)\left(\dfrac{1}{4}\right)\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{4}\right)}{\left(\dfrac{1}{3}-\dfrac{1}{5}\right)\left(\dfrac{1}{3}+\dfrac{1}{4}\right)}[/tex]

When multiplying fractions, simply multiply the numerators and the denominators:

[tex]\implies \dfrac{60 \left(\dfrac{1 \cdot -1 \cdot 1}{3\cdot 5 \cdot 4}\right)\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{4}\right)}{\left(\dfrac{1}{3}-\dfrac{1}{5}\right)\left(\dfrac{1}{3}+\dfrac{1}{4}\right)}[/tex]

[tex]\implies \dfrac{60 \left(-\dfrac{1}{60}\right)\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{4}\right)}{\left(\dfrac{1}{3}-\dfrac{1}{5}\right)\left(\dfrac{1}{3}+\dfrac{1}{4}\right)}[/tex]

[tex]\implies \dfrac{\left(-1\right)\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{4}\right)}{\left(\dfrac{1}{3}-\dfrac{1}{5}\right)\left(\dfrac{1}{3}+\dfrac{1}{4}\right)}[/tex]

When adding or subtracting fractions, make the denominators the same:

[tex]\implies \dfrac{\left(-1\right)\left(\dfrac{20}{60}-\dfrac{12}{60}+\dfrac{15}{60}\right)}{\left(\dfrac{5}{15}-\dfrac{3}{15}\right)\left(\dfrac{4}{12}+\dfrac{3}{12}\right)}[/tex]

Now add the numerators and put that over the denominator:

[tex]\implies \dfrac{\left(-1\right)\left(\dfrac{20-12+15}{60}\right)}{\left(\dfrac{5-3}{15}\right)\left(\dfrac{4+3}{12}\right)}[/tex]

[tex]\implies \dfrac{\left(-1\right)\left(\dfrac{23}{60}\right)}{\left(\dfrac{2}{15}\right)\left(\dfrac{7}{12}\right)}[/tex]

Again, multiply the fractions:

[tex]\implies \dfrac{\left(-1 \cdot \dfrac{23}{60}\right)}{\left(\dfrac{2 \cdot 7}{15 \cdot 12}\right)}[/tex]

[tex]\implies \dfrac{-\dfrac{23}{60}}{\dfrac{14}{180}}[/tex]

To divide the fractions, turn the second fraction upside down, then multiply it by the first fraction:

[tex]\implies -\dfrac{23}{60} \cdot \dfrac{180}{14}[/tex]

[tex]\implies -\dfrac{4140}{840}[/tex]

Finally, simplify:

[tex]\implies -\dfrac{4140 \div 60}{840 \div 60}[/tex]

[tex]\implies -\dfrac{69}{14}[/tex]

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