Answer:
Step-by-step explanation:
In the equation
![(1)/(R)=(1)/(R_1)+(1)/(R_2)](https://img.qammunity.org/2023/formulas/mathematics/college/ljj73mk7q0f2k5roug0t0lpf5npxp3ku1t.png)
we out in R = 12 and R_2 = 21 to get
![(1)/(12)=(1)/(R_1)+(1)/(21)](https://img.qammunity.org/2023/formulas/mathematics/college/mpixf021kjonrx4bwz2nsvzhx2f4qs76q8.png)
Subtracting 1/21 from both sides gives
![(1)/(12)-(1)/(21)=(1)/(R_1)](https://img.qammunity.org/2023/formulas/mathematics/college/n1u7zhs1b36c2ji6hw4o52f7y31p3xetpd.png)
We subtract the fractions on the left-hand side to get
![(1\cdot21)/(12\cdot21)-(1\cdot12)/(21\cdot12)](https://img.qammunity.org/2023/formulas/mathematics/college/fhc9gjqz2xpola7yl75q94pfn4aclt993t.png)
![=(9)/(252)=(1)/(28)](https://img.qammunity.org/2023/formulas/mathematics/college/35uy28a8o77l64irqee8xsk3yist4esr5e.png)
Hence,
![(1)/(28)=(1)/(R_1)](https://img.qammunity.org/2023/formulas/mathematics/college/7v5pfa6amko99sn0wtpxe6ufvpletzkrqo.png)
Taking the reciprocal of both sides gives
![R_1=28](https://img.qammunity.org/2023/formulas/mathematics/college/pippwatyevcnsxowxqig727m8an6i0lift.png)
Which is our answer!