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Let x=numerator of original fraction
And let y=denominator of original fraction
We are told that:
(x-3)/(y-3)=4/5 multiply each side by 5(y-3)
5(x-3)=4(y-3) get rid of parens
5x-15=4y-12 subtract 4y from and add 15 to both sides
5x-15+15-4y=4y-4y-12+15 collect like terms
5x-4y=3---------------------------------------------eq1
We are also told that:
(x+3)/(y+3)=7/8 multiply each side by 8(y+3)
8(x+3)=7(y+3) get rid of parens
8x+24=7y+21 subtract 7y and also 24 from both sides
8x-7y+24-24=7y-7y+21-24 collect like terms
8x-7y=-3------------------------------------------eq2
Multiply each term in eq1 by 8
40x-32y=24-----------------------------------eq1a
Multiply each term in eq2 by 5
40x-35y=-15-------------------------------------eq2a
subtract eq1a from eq2a
-3y=-39 divide both sides by -3
y=13--------------------------------------denominator of original fraction
Substitute y=13 into eq1
5x-4*13=3
5x-52=3 add 52 to both sides
5x-52+52=3+52 collect like terms
5x=55 divide both sides by 5
x=11-------------------------------------numerator of original fraction
CK
(11-3)/(13-3)=4/5
8/10=4/5
4/5=4/5
also
(11+3)/(13+3)=7/8
14/16=7/8
7/8=7/8
Hope this helps----ptaylor
