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I have values for X, Y and B and the lab manual has asked "Using the approximated, simplified expressions for X (equation 2), Y (equation 3) and B (equation 4), determine K

_{cat}, [E]

_{0act}and K

_{2}/K for each kinetic experiment.

From these values, determine K

_{m}and p."

I have calculated K

_{cat}, [E]

_{0act}and K

_{2}/K, but can't work out how to determine K

_{m}.

the simplified equations are -

equation 2 is simplified to x ≈ K

_{cat}.[E]

_{0act}(if [ S] >>k

_{m})

equation 3 is simplified to y ≈ [E]

_{0act}(if [ S] >>K

_{m}and K

_{2}>>K

_{3})

equation 4 is simplified to B ≈ K

_{2}[ S]/K (if [ S]>>K

_{m}and K

_{2}>>K

_{3})

where K

_{cat}= K

_{2}K

_{3}/(K

_{2}+K

_{3}) ≈ K

_{3}(if K

_{2}>>K

_{3})

K

_{m}= K

_{3}K/(K

_{2}+K

_{3})

the lab manual suggests "to determine K

_{m}, consider how K

_{2}/K can be derived from the expressions for

K

_{cat}and K

_{m}."

I'm lost and not sure how to solve for K

_{m}. I have spent hours on it and just don't understand what it is I'm supposed to do.