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"widen the difference" is correct and can be used in written English.
It means to increase the gap or contrast between two things. It can be used in a variety of contexts, such as describing a change in opinions, attitudes, or outcomes. Example: The new policies implemented by the government have widened the difference between the rich and the poor, leading to increased social inequality.
Exact(5)
One document discussed how a deal in which one subsidiary, El Paso Natural Gas, sold pipeline capacity to a sister company, El Paso Merchant Energy, would allow the company to "widen" the difference between what gas could be bought for in Texas and New Mexico and what it could be sold for in California.
In Scotland such taxes are now about 10% lower than in England and this move will widen the difference.In this section When the credit dries up Taking shape Troubled waters Stalking the land A MacTax haven in the making?
However, inclusion of these costs would only widen the difference in medication costs for these two groups making the unstable group even more costly.
As plaque builds in the infrarenal aorta, the increased blood velocity through this segment can widen the difference between pressures sensed at the iliac and the renal artery bifurcations.
He ought to pick out and widen the difference between the regime in Tehran and the people of Iran.
Similar(55)
In addition to differences in socio-economic endowment, residential segregation and school system characteristics, such as tracking (Entorf & Lauk 2008; Cobb-Clark et al. 2012), tend to widen the differences in schooling outcomes between migrants and natives.
Qwest Communications International raised its bid for MCI on Thursday, widening the difference with a competing offer from Verizon Communications.
As it will be shown in the next section, considering the total indirect effects widens the difference between the gross bilateral balances of trade and the value-added bilateral balances, mostly because of the way each NAFTA member is integrated with the rest of the world.
The shift has driven up costs and widened the difference between wholesale prices in California and other markets, according to U.S. Department of Agriculture economists.
The ATP decline in the untreated control cells leveled off statistically, widening the difference in the ATP levels between the two treatment groups.
Therefore, a right-to-left shunt widens the difference between alveolar carbon dioxide tension (PaCO2) and PaCO2, which defines the alveolar dead space (see Equation 1, below).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com