Question

Hi, could you help me with this substitution question?

I'd really appreciate if you added workings out as I'm terribly confused.
Thanks,

Answer 1

`-(69)/(14)`

Explanation:

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

`\implies (60 \left((1)/(3)\right)\left(-(1)/(5)\right)\left((1)/(4)\right)\left((1)/(3)-(1)/(5)+(1)/(4)\right))/(\left((1)/(3)-(1)/(5)\right)\left((1)/(3)+(1)/(4)\right))`

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

`\implies (60 \left((1 \cdot -1 \cdot 1)/(3\cdot 5 \cdot 4)\right)\left((1)/(3)-(1)/(5)+(1)/(4)\right))/(\left((1)/(3)-(1)/(5)\right)\left((1)/(3)+(1)/(4)\right))`

`\implies (60 \left(-(1)/(60)\right)\left((1)/(3)-(1)/(5)+(1)/(4)\right))/(\left((1)/(3)-(1)/(5)\right)\left((1)/(3)+(1)/(4)\right))`

`\implies (\left(-1\right)\left((1)/(3)-(1)/(5)+(1)/(4)\right))/(\left((1)/(3)-(1)/(5)\right)\left((1)/(3)+(1)/(4)\right))`

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

`\implies (\left(-1\right)\left((20)/(60)-(12)/(60)+(15)/(60)\right))/(\left((5)/(15)-(3)/(15)\right)\left((4)/(12)+(3)/(12)\right))`

Now add the numerators and put that over the denominator:

`\implies (\left(-1\right)\left((20-12+15)/(60)\right))/(\left((5-3)/(15)\right)\left((4+3)/(12)\right))`

`\implies (\left(-1\right)\left((23)/(60)\right))/(\left((2)/(15)\right)\left((7)/(12)\right))`

Again, multiply the fractions:

`\implies (\left(-1 \cdot (23)/(60)\right))/(\left((2 \cdot 7)/(15 \cdot 12)\right))`

`\implies (-(23)/(60))/((14)/(180))`

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

`\implies -(23)/(60) \cdot (180)/(14)`

`\implies -(4140)/(840)`

Finally, simplify:

`\implies -(4140 / 60)/(840 / 60)`

`\implies -(69)/(14)`