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GB-41-03-001 · Rearranging a rational formula

Make x the subject of y=8x+12x−7y=\frac{8x+12}{x-7}. State the excluded value of y.

Rearranging Formula: Subject Appears Twice Booklet p. 29
Method
1) Multiply
2) Expand
3) Rearrange
4) Factorise
5) Divide
Worked Example (GB-41-03-001)
1)
Multiply by the denominator: y(x−7)=8x+12y(x-7)=8x+12.
2)
Expand: xy−7y=8x+12xy-7y=8x+12.
3)
Rearrange, keeping all terms containing x on the left: xy−8x=7y+12xy-8x=7y+12.
4)
Factorise: x(y−8)=7y+12x(y-8)=7y+12.
5)
Divide: x=7y+12y−8x=\frac{7y+12}{y-8}. The denominator cannot be zero, so y≠8y\ne8.
Ans = x=7y+12y−8x=\frac{7y+12}{y-8}, y ≠ 8.